Solving Systems of Equations

Find the point of intersection for; y=⁻6x+5 y=4x-5

(1,⁻1)

Find the point of intersection for; y=3x-3 y=⁻3x+9

(2,3)

Find the point of intersection for; y=(1/2)x-3.5 y=3x-11

(3,-2)

Find the point of intersection for; y=⁻x+4 y=⁻(2/3)x+3

(3,1)

Find the point of intersection for; y=2x-5 y=⁻3x+15

(4,3)

Find the point of intersection for; y=(3/4)x-4 y=x-5

(4,⁻1)

Find the point of intersection for; y=⁻2x+2 y=⁻1.5x+2.5

(⁻1,4)

Find the point of intersection for; y=2.5x+4 y=5x+9

(⁻2,⁻1)

Find the point of intersection for; y=(3/2)x+3 y=⁻3x-15

(⁻4,⁻3)

What does x equal? 7-5x=28+2x

-3

What does y equal? 5-2y=-3y-2

-7

What does x equal? 3x-9=x-1

4

Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can Margie spend on each dog for food and medication?

Let c = cost per cat 164c + 24d = 4240 Let d = cost per dog d = 2c Solve by any method mentioned. If done algebraically with substitution: 164c + 24d = 4240 d = 2c 164c + 24(2c) = 4240 164c + 48c = 4240 212c = 4240 c = 20 She can spend $20 on each cat. d = 2c d = 2(20) = 40 She can spend $40 on each dog.

Bill and Steve decide to spend the afternoon at an amusement park enjoying their favorite activities, the water slide and the gigantic Ferris wheel. Their tickets are stamped each time they slide or ride. At the end of the afternoon they have the following tickets: Fun Time Amusements Water Slide: *** Ferris Wheel: *** Total: $17.70 Bill's Ticket Fun Time Amusements Water Slide: ** Ferris Wheel: *** Total: $15.55 Steve's Ticket How much does it cost to ride the Ferris Wheel? How much does it cost to slide on the Water Slide?

Let w = cost of water slide 3w + 3f = 17.70 Let f = cost of Ferris wheel 2w + 3f = 15.55 Solve by any method mentioned. If done algebraically: 3w + 3f = 17.70 2w + 3f = 15.55 w = 2.15 The water slide costs $2.15 per slide. Substitute: 2(2.15) + 3f = 15.55 4.30 + 3f = 15.55 3f = 11.25 f = 3.75 The Ferris wheel costs $3.75 per ride.

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

Let x = T/F questions x + y = 20 Let y = Multiple Choice questions 3x + 11y = 100 Solve by any method mentioned. If done algebraically: x + y = 20 3x + 11y = 100 3(x + y = 20) 3x + 11 y = 100 3x + 3y = 60 3x + 11y = 100 -8y = -40 8y = 40 y = 5 There are 5 multiple choice questions. x + 5 = 20 x = 15 There are 15 T/F questions.

Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?

Let x = small pitcher 2x + y = 8 y - x = 2 y = large pitcher Solve by any method mentioned. If done algebraically: 2x + y = 8 -x + y = 2 subtract: 3x = 6 x = 2 The small pitcher holds 2 cups of water. 2(2) + y = 8 4 + y = 8 y = 4 The large pitcher holds 4 cups of water.

Is the ordered pair (-4,0) a solution? Yes/No? y = .5x + 2 y = ⁻(4/3)x + 2?

No

Is the ordered pair (1/2,⁻2/3) a solution?Yes/No? y = 4x - (8/3) y = 6x - (5/3)?

No

Is the ordered pair (2,-1) a solution? Yes/No? y=⁻0.75x+0.5 y=⁻1.5x+5

No

Is the ordered pair (2,⁻6) a solution? Yes/No? 3.5x+2.5y=⁻8 1.5x-3.5y=22

No

Is the ordered pair (4,8) a solution? Yes/No? y=2x y=⁻4x+12

No

The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert tickets sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket?

Solve the system simultaneously. Various methods of solution can be used. One method is shown here. 5x + 2y = 48 3x + 2y = 32 subtracting gives: 2x = 16 and x = 8. The cost of an adult ticket is $8.

Is the ordered pair (3,⁻2) a solution?Yes/No? y = ⁻5x + 13 y = (7/3)x - 9?

Yes

Is the ordered pair (4,3) a solution?Yes/No? y = .5x + 1 y = .6x + 0.6

Yes

Is the ordered pair (5,⁻3) a solution? Yes/No? y = -.75x + 0.75 y = ⁻(2/3)x + (1/3)

Yes

Is the ordered pair (6,⁻2) a solution? Yes/No? y=0.5x-5 y=⁻(1/3)x

Yes

Is the ordered pair (⁻2,⁻2) a solution? Yes/No? 7x+2y=⁻18 3x-5y=4

Yes

Is the ordered pair (⁻3,⁻2) a solution? Yes/No? 2x-5y=4 x-3y=3

Yes

Is the ordered pair (⁻3.5,⁻1.5) a solution? Yes/No? y = 2.5x + 7.25 y = ⁻2.5x - 10.25

Yes