Algebra 1 9th - 5

Intersecting lines = lines meet and the solution is where (x, y) meet (point of intersection).

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Solving systems by graphing: solution must satisfy both equations. Graph each equation by plotting the "x" intercept and the "y" intercept. Label each line and determine the solution at the point of intersection.

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Is the ordered pair a solution or no solution: 2x - 8y = 9 (1/2, - 1) 6x + 2y = 1 1. Solution 2. No Solution

2 (1/2) - 8(- 1) = 9 1 + 8 = 9 6(1/2) + 2(- 1) = 1 3 - 2 = 1 Solution

Is the ordered pair a solution or no solution: 2x - 7y = 11 (2, -1) 3x + 5y = 1 1. Solution 2. No Solution

2(2) - 7(- 1) = 11 4 + 7 = 11 3(2) + 5 (- 1) = 1 6 - 5 = 1 Solution

Solve system by elimination: 35x + 28y = 56 12x + 28y = 56

35 x + 28y = 56 -12x - 28Y = - 56 _____________________ 23x = 0 x = 0 35(0) + 28y = 56 y = 2 (0, 2)

Solve system by elimination: 3x - 4y = 26 5x + 4y = 38

3x - 4y = 26 5x + 4y = 38 _________________ 8x = 64 | x = 8 5(8) - 4y = 38 40 + 4y = 38 4y = - 2 y = - 1/2 (8, - 1/2)

Is the ordered pair a solution or no solution: 4x - 5y = - 10 (5, 6) 7x - 3 = 17 1. Solution 2. No Solution

4(5) - 5(6) = 10 20 - 30 = - 10 - 10 7(5) - 3(6) = 17 35 - 18 = 17 Solution

Solve system by elimination: 2x + 4y = 4 3x - 6y = 12

6x + 12y = 12 6x - 12y = 24 ___________________ 12x = 36 x = 3 2(3) + 4y = 4 6 + 4y = 4 4y = - 2 y = - 1/2 (3, - 1/2)

Is the ordered pair a solution or no solution: 9x + 4y = 21 (-3, 12) 3x - y = - 3 1. Solution 2. No Solution

9(- 3) + 4(12) = 21 - 27 + 48 = 21 3(- 3) - 12 = - 3 -9 - 12 "is not equal to" -3 No Solution

Solve system by graphing: 2x - 6y = 12 x + y = 12

Use the "T" table: x | y -6 | -4 0 | -2 6 | 0 x | y 0 | 2 2 | 0 4 | -2 Graph and solve the point of intersection.

A system of _____________ lines does not intersect.

parallel

An inconsistent system of equations has no solution. True or False

true

The solution to a system of equations is an ordered pair. True or False

true

To eliminate the "y terms" from the following system of equations, the first equation must be multiplied by 5 and the second equation must be multiplied by 4. x - 4y = 11 -3x + 5y = 25 True or False

true

Solve system by substitution: x + 4y = - 10 2x - y = 7

x = - 4y - 10 2(- 4y - 10) - y = 7 - 8y - 20 - y = 7 - 9y = 27 y = - 3 x + 4(- 3) = - 10 x - 12 = - 10 x = 2 (2, - 3)

Solve using a system of equations: There are 32 students in Cody's class. If there were twice as many girls in the class, the total number of students would be 45. How many girls are in Cody's class?

x = girls y = boys x + y = 32 - x - y = - 32 2x + y = 45 2x + y = 45 ____________________ x = 13 13 girls

Solve using a system of equations: The local music activities coordinator sold 300 tickets to the orchestra concert. Student tickets were $4, and adult tickets were $6. If the total sales were $1,600, how many student tickets were sold?

x = student tickets y = 300 - x y = adult tickets x + y = 300 4x + 6(300 - x) = 1,600 4x + 6y = 1,600 4x + 1,800 - 6x = 1,600 -2x = -200 x = 100 100 student tickets

Solve system by graphing: x + 3y = 6 2x - 4y = 12

y = - 1/3x + 2 y = 1/2x - 3 Graph and solve the point of intersection.

Solve system by substitution: 2x + 3y = 7 x + y = 3

y = 3 - x 2x + 3(3 - x) = 7 2x + 9 - 3x = 7 - x = - 2 x = 2 2 + y = 3 y = 1 (2, 1)

Solve system by substitution: x - y = 4 4y - x = 14

y = x - 4 4(x - 4) - x = 14 4x - 16 - x = 14 3x = 30 x = 10 10 - y = 4 -y = - 6 y = 6 (10, 6)