Question

-2x + 6y = 6
-7x + 8y = -5

-2x - y = -9
5x - 2y = 18

Explanation:

First System: $-2x + 6y = 6$ and $-7x + 8y = -5$

Step1: Simplify first equation

Divide first equation by 2: $-x + 3y = 3$ → $x = 3y - 3$

Step2: Substitute $x$ into second equation

$-7(3y - 3) + 8y = -5$ → $-21y + 21 + 8y = -5$ → $-13y = -26$

Step3: Solve for $y$

$y = \frac{-26}{-13} = 2$

Step4: Find $x$

$x = 3(2) - 3 = 3$

Second System: $-2x - y = -9$ and $5x - 2y = 18$

Step1: Isolate $y$ from first equation

$-y = 2x - 9$ → $y = -2x + 9$

Step2: Substitute $y$ into second equation

$5x - 2(-2x + 9) = 18$ → $5x + 4x - 18 = 18$ → $9x = 36$

Step3: Solve for $x$

$x = \frac{36}{9} = 4$

Step4: Find $y$

$y = -2(4) + 9 = 1$

Answer:

$x=3$, $y=2$