Question

independent practice
graph each system of equations to find its solution. then
to both equations. be sure to show all work.

1. ( y = -x + 6 ) and ( y = \frac{2}{3}x - 9 )

solution:
✓check:

1. ( y )

solut

1. ( y = 3x - 4 ) and ( y = -\frac{1}{2}x + 10 )

4.

Explanation:

Step1: Set equations equal

$-x + 6 = \frac{2}{3}x - 9$

Step2: Multiply by 3 to eliminate fraction

$-3x + 18 = 2x - 27$

Step3: Isolate x terms

$-3x - 2x = -27 - 18$
$-5x = -45$

Step4: Solve for x

$x = \frac{-45}{-5} = 9$

Step5: Find y with x=9

$y = -(9) + 6 = -3$

Step6: Check first equation

$y = -9 + 6 = -3$

Step7: Check second equation

$y = \frac{2}{3}(9) - 9 = 6 - 9 = -3$

Step1: Set equations equal

$3x - 4 = -\frac{1}{2}x + 10$

Step2: Multiply by 2 to eliminate fraction

$6x - 8 = -x + 20$

Step3: Isolate x terms

$6x + x = 20 + 8$
$7x = 28$

Step4: Solve for x

$x = \frac{28}{7} = 4$

Step5: Find y with x=4

$y = 3(4) - 4 = 8$

Step6: Check first equation

$y = 3(4) - 4 = 8$

Step7: Check second equation

$y = -\frac{1}{2}(4) + 10 = -2 + 10 = 8$

Answer:

Solution: $(9, -3)$

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