algebra 1a - unit 3: linear systems and inequalities

what is the solution for the system of equations {9x + 8y = 3, 6x - 12y = -11}?

(-1/3,3/4)

what is the solution to the system of equations {3x + y = -18, 5x + 3y = 2}?

(-14, 24)

what values of x and y satisfy the system of equations {2x + 1/2y = -17, 3x + 2y = 7}?

(-15,26)

solve the system of equations {y = 15x + 9, y = 1/2x - 20}. what is the solution to the system?

(-2,-21)

what values of x and y satisfy the system of equations {10x = 5y - 8, 15x = -5y - 2}?

(-2/5,4/5)

what is the solution to the system of equations {-3x + 5y = 12, 7x - 5y = -28}?

(-4, 0)

what values of x and y satisfy the system of equations {x = -2y + 1, 3x + 8y = 11}?

(-7,4)

what is the solution to the system of equations {-2x + 4y = 1, -4x + 3y = 12}?

(-9/2, -2)

find the solution to the following system of equations: {x + 2y = -1, 2x - 3y = 5}

(1, -1)

what values of x and y satisfy the system {y = -2x + 3, y = 5x - 4}?

(1,1)

what values of x and y satisfy the system of equation {10x + 3y = -5, -5x - 4y = 10}?

(2/5, -3)

what values of x and y satisfy the system of equations {3x + 2y = 14, x = 4y - 2}?

(26/7, 10/7)

what is the solution for the system of equations {4x - 3y = 3, 6x - 2y = 4}?

(3/5,-1/5)

what is the solution for the system of equations {3x + 2y = 10, 2x + 3y = 5}?

(4, -1)

what is the y-valuey-value of the solution to the system of equations {3x + 4y = 4, 2x − 4y = 6}?

-1/2

what values of x and y satisfy the system of equations {8x + 9y = -3, 6x + 7y = 1}?

(-15,13)

lesson 14

linear inequalities in two variables

what is the solution for the system of equations {-8x + 4y = -2, 4x - 2y = 1}?

inf

troy signed up for a new cell phone plan which charges him a fee of $40 per month, plus $0.05 for each text message (t) that he sends. if troy wants to spend at most $70 on his cell phone bill this month, which inequality below can be used to determine the number of text messages that he can send?

$40 + $0.05t ≤ $70

anton wants to plant a small orchard of apple trees and cherry trees in his back yard. he has a budget of $1,000 and his plot has a maximum of 100 square feet. the apple trees he wants cost $40 each and require 5 square feet. the cherry trees he wants cost $50 each and require 4 square feet. which system of inequalities correctly represents this situation where a is the number of apple trees and c is the number of cherry trees that anton can plant in his orchard?

{5a + 4c ≤ 100 {40a + 50c ≤ 1000

jaime is at a library that is 5 miles from her house. her brother, max, is at a rec center that is 4.5 miles from the house. the library and rec center both close at 6:00 p.m. jaime and max are beginning their training for soccer, so they decide to run home. jaime maintains a constant rate of 8 miles per hour, while max runs at a constant rate of 7.5 miles per hour. which system of equations correctly represents these situations where d is the distance from home in miles and t is the length of time in hours?

{d = -8t + 5 {d = -7.5t + 4.5

this year, when latifa and jameel add their ages, the sum is 29. latifa's age is 10 less than twice Jameel's age. which system of equations correctly represents this situation where l is latifa's age and j is jameel's age?

{l + j = 29 {l = 2j - 10

lina is older than her cousin sarika. this year, the sum of their ages is 31, and the difference between their ages is 5. which system of equations correctly represents this situation where l represents lina's age and s represents sarika's age?

{l + s = 31 {l - s = 5

moira has a collection of nickels (5 cents) and dimes (10 cents). she has 630 coins totaling a value of $48. which system of equations correctly represents this situation where n represents the number of nickels moira has and d represents the number of dimes she has?

{n + d = 630 {0.05n + 0.10d = 48

maggie and reggie make necklaces to sell at craft shows. maggie still has 7 necklaces left over from the last craft show, and she can make 2 necklaces every hour. reggie still has 4 necklaces left from the last craft show, and he can make 2 necklaces every hour. which system of equations correctly represents this situation where n represents the number of necklaces and h represents the number of hours spent making necklaces?

{n = 2h + 7 {n = 2h + 4

the sum of two numbers is 22. the difference between the larger number and the smaller number is 46. which system of equations correctly represents this situation where x represents the larger number and y represents the smaller number?

{x + y = 22 {x - y = 46

match each system of inequalities with the graph that represents its solution set.

{y ≤ 1/2x − 3, y < −4x + 1} : https://cdstools.flipswitch.com/asset/media/940994 {y ≥ 1/2x − 3, y < −4x + 1} : https://cdstools.flipswitch.com/asset/media/940993 {y ≤ 1/2x − 3, y > −4x + 1} : https://cdstools.flipswitch.com/asset/media/940996 {y ≥ 1/2x − 3, y > −4x + 1} : https://cdstools.flipswitch.com/asset/media/940997

liam wants to plant a small orchard with apples and cherries in a 62-square-foot plot, and he has a budget of $345 for purchasing trees. the apple trees he wants cost $30 each and require 8 square feet each for maximum fruit production. the cherry trees he wants cost $45 each and require 6 square feet for maximum fruit production. if he sells all the fruit, he is able to earn $90 per apple tree and $120 per cherry tree. which points are the extreme points for the solution set for this situation? select all that apply.

0.13 of 1 (0, 10.33) (7.75, 0)

answer the following question by using this graph of the system of inequalities {y ≥ 5/2x − 1, y > −1/3 + 1}. which points are in the solution set for the system? select all that apply.

0.17 of 1 (2, 4) (-3, 2)

what value of y satisfies the system of equations {9x + 2y = 24, y = 6x + 19}?

15

shanice has budgeted $175 for new clothes. she decides to buy a pair of shoes that cost $47 and then buys some $18 shirts. which inequality represents this situation where s is the number of shirts she can buy?

18s + 47 ≤ 175

what value of x satisfies the system of equations {2x + 5y = 35, x = -10 - 15y}?

23

lakita is going to plant trees and bushes to landscape her new yard. she cannot exceed her budget of $150. each tree costs $45, and each bush costs $20. which inequality correctly represents the situation, where t is the number of trees and b is the number of bushes lakita purchases?

45t + 20b ≤ 150

taylor has $150 to spend on small canvases and paints for her art classes. the art supply store sells a four-pack of small canvases for $4.00 and paints for $6.25, including tax. which inequality represents this situation where c is the number of four-packs of canvases and pis the number of paints taylor purchases?

4c + 6.25p ≤ 150

match each inequality with the graph of its solution.

5(x + 3) - 8 < 17 : https://cdstools.flipswitch.com/asset/media/926288 3 + 5x ≥ 7 + 3x : https://cdstools.flipswitch.com/asset/media/926292 4 - 1/2x < 5 : https://cdstools.flipswitch.com/asset/media/926293 3(x + 10) ≤ 24 : https://cdstools.flipswitch.com/asset/media/926295

on monday, josh went to the farmer's market. he bought 5 peaches and 2 watermelons for $7.75. on thursday, josh went back to the farmer's market and bought 3 peaches and 4 watermelons for $10.95. which of the following systems of equations can be used to determine the cost for one peach (p) and one watermelon (w)?

5p + 2w = $7.75 3p + 4w = $10.95

the pirouette dance team needs more than $300 to cover costume expenses. they have $75 and plan to sell raffle tickets for $5 each in order to raise money. which inequality represents the situation where r is the number of raffle tickets the team needs to sell?

5r + 75 > 300

a library has at least 900 square feet to create a new study area. each study cubicle uses 6 square feet, and each computer station uses 8 square feet. which inequality correctly represents this situation, where s is the number of study cubicles and c is the number of computer stations?

6s + 8c ≥ 900

match each inequality with the graph of its solution.

8 - 5(x + 2) < -5 : https://cdstools.flipswitch.com/asset/media/929979 2(5x − 3) ≥ −12 : https://cdstools.flipswitch.com/asset/media/929980 2(x − 3) < 3x − 1 : https://cdstools.flipswitch.com/asset/media/929981

sasha reads at a rate of 0.8 pages per minute in her favorite novel, but only 0.5 pages per minute in the autobiography she is currently reading. her english class has a minimum reading requirement of at least 75 pages per week. this situation is represented by the inequality 0.8n + 0.5a ≥ 75, where n is the number of minutes she reads her novel and a is the number of minutes she reads the autobiography. which statement correctly explains a solution for this situation?

if sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.

in order to create a system of equations that has the same solution as the system {x + y = 4, 2x + y = 7}, complete three steps. match each blank with the system or statement that correctly fills in that blank.

blank a : -1 to get the equation -x + -y = -4 blank b : -x - y = -4 to get the equation x = 3 blank c : {x + y = 4, x = 3}

daisy is building a rectangular pen for her chickens along one wall in her back yard. she needs to build a fence along the remaining three sides of the pen. she represents this situation with the inequality w + 2l ≤ 125. which explanation correctly interprets this inequality?

daisy has one side of the rectangular pen along the wall, so she needs one width, w, and two lengths, 2l. she has at most 125 feet of fencing materials to build the fence for her pen.

adam is creating an animated short film, and he needs 24 frames per second of film. he already has at least 250 frames. which inequality represents this situation where f is the number of frames and s is the number of seconds of film?

f ≥ 2s + 250

corliss earns an hourly wage, as well as tips, each day he works. his daily earned income, m, after h hours can be represented by the inequality m > 11h + 35. which answer choice correctly describes the inequality?

he makes more than $11 per hour plus $35 in tips.

which graph correctly represents the solution for the inequality 12 < 2(25 − x)?

https://cdstools.flipswitch.com/asset/media/1154851

which graph represents the solution set for the inequality y ≥ x + 1?

https://cdstools.flipswitch.com/asset/media/930116

which graph represents the solution set for the inequality y < 4 - 2?

https://cdstools.flipswitch.com/asset/media/930140

what is the graph of the linear inequality y ≤ −3x + 4?

https://cdstools.flipswitch.com/asset/media/933646

the inequality 2x + 5 < y describes which of the following graphs?

https://cdstools.flipswitch.com/asset/media/933666

charlotte is knitting hats and scarves to sell on her online store. she has 20 balls of yarn and needs one-half a ball for each hat and a full ball for each scarf. what combination of hats and scarves allows charlotte to maximize her profit?

if charlotte makes 22 hats and 0 scarves, she will have a maximum profit of $176.

the equation that represents the total money (m) that liam earns from selling all the fruit from his trees is m = 90x + 120y. what combination of trees allows liam to maximize his income?

if liam plants 4 apple trees and 5 cherry trees, he will have a maximum income of $960.

what is the solution for the system of equations {6x + 3y = 15, 8x + 4y = 20}?

inf

what is the solution to the system of equations {y = 4/5x + 7/2, y = 0.8x + 3.5}?

infinitely many solutions

lesson 13

linear inequalities in one variable

a system of linear equations is shown below. 2x + 4y = 10 3x - y = 8 maria is attempting to prove that by replacing 2x + 4y = 10 with a different equation it will sometimes produce a new system of equations with the same solution. maria plans on multiplying 2x + 4y = 10 by 2 and then adding the results to the equation 3x − y = 8 in order to create a new equation. maria claims that the new equation that she will replace 2x + 4y = 10 with is 7x + 7y = 12. is maria correct?

maria is not correct because the new equation should be 7x + 7y = 28.

what values of x and y satisfy the system {y = 3x + 2, y = 3x - 6}?

no

what values of x and y satisfy the system of equations {4x - 3y = 8, -4x + 3y = 8}?

no solution

use the following graph of the system of inequalities {y ≤ 3x − 2, y ≥ −1/2x to answer the question. which region represents the solution set for the system of inequalities?

region 1

lesson 12

solving linear systems by elimination

lesson 11

solving linear systems by substitution

lesson 15

systems of linear inequalities

melanie wants to rent a bike on her vacation for less than $50. at mike's bike shop, she can rent a bike for $8 per hour plus a $6 flat fee. any portion of an hour is charged as a full hour. the inequality that represents this situation is 8h + 6 < 50, where h represents the number of hours melanie rents the bike. what does the solution for the inequality mean in relation to the situation

the solution h < 5.5 means that melanie can rent the bike for no more than 5 hours.

jachin is saving to buy a new tablet that costs more than $400. he already has $85 in his piggy bank, and he is able to put $25 in his bank once a week when he gets paid for mowing lawns. the inequality that represents this situation is 25w + 85 > 400, where ww represents the number of weeks jachin makes a deposit into his piggy bank. what does the solution for the inequality mean in relation to this situation?

the solution is w > 12.6. it will take jachin a minimum of 13 weeks to save enough money to buy the tablet.

lydia needs to buy both lanterns and streamers for a party, and she has a maximum budget of $15 for these decorations. each lantern costs $7, and each pack of streamers costs $5. the following graph shows the solution set for the inequality that represents this situation, where x is the number of lanterns and y is the number of streamers lydia can purchase. which description correctly interprets the solution set for this situation?

the solution set for this situation includes only one answer. since she can't buy a fractional or negative number of lanterns or packs of streamers, the only solution for the situation is to purchase one of each item.

a situation can be represented by the system of inequalities {2.5x + 8y ≤ 40, x + y ≤ 10, where x is the number of pounds of almonds and y is the number of pounds of cashews. which statement correctly describes the solution set for this situation?

the solutions for this situation are any real number values for x and y that are in the shaded region, including the segments that enclose that region.

the all-stars softball team needs to purchase new uniform jerseys. the manager uses the inequality d ≤ 750 to determine how much money the team can spend per jersey. which description correctly interprets the inequality in terms of this situation?

the team has no more than $750 to spend on jerseys.

wilmer spends at least 13 hours reading for his assignments each week, plus 1 hour completing each reading response assignment. the inequality that represents the total number of hours, y, wilmer spends on his various assignments each week is y ≥ x + 13, where x represents the number of reading response assignments he completes. this week, wilmer can spend only 5 hours total reading for his various assignments. which explanation correctly analyzes whether there is a solution for this scenario?

there is no solution. for the inequality to be true, the value of x has to be negative. this is impossible because wilmer can't have a negative number of reading response assignments.

what is the solution for the inequality 5 − 3x > 26?

x < -7 (no spaces pls)

solve the linear inequality below. 9x − 8 > 4x + 7

x > 3 (no spaces)

what is the solution for the inequality 14 − 3(x + 5) ≤ −13?

x ≥ 4

match each inequality with the graph of its solution set.

y ≥ −1/2x + 3 : https://cdstools.flipswitch.com/asset/media/930122 y ≤ −3/5x + 3 : https://cdstools.flipswitch.com/asset/media/930124 y > −2x + 3 : https://cdstools.flipswitch.com/asset/media/930125 y < −5/3x + 3 : https://cdstools.flipswitch.com/asset/media/930126

in order to create a system of equations with the same solution as the system, camilo multiplied both sides of the second equation by a number, added the new equation to the first equation, and replaced the first equation with the result. which system of equations could be camilo's new system?

{-3x - y = -18 {2x + y = 14

amanda sews t-shirts and sweatshirts to earn money. it costs her $3 to make each t-shirt and $5 to make each sweatshirt. this month she has budgeted $150 for materials for the shirts. it takes amanda 2 hours to sew a t-shirt and 1 hour to sew a sweatshirt, but because she is booked with other projects for the month she only has 50 hours to sew the shirts. which system of inequalities represents this situation, where t represents the number of t-shirts and ss represents the number of sweatshirts that amanda can sew?

{3t + 5s ≤ 150 {2t + s ≤ 50