Question

solve the following system of equations.
$-9x - 5y = -10$
$8x - 7y = -14$
$x = \square$
$y = \square$

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 8: $8(-9x -5y)=8(-10) \implies -72x -40y = -80$
Multiply second eq by 9: $9(8x -7y)=9(-14) \implies 72x -63y = -126$

Step2: Add scaled equations

Add the two new equations to eliminate $x$:
$(-72x -40y) + (72x -63y) = -80 + (-126)$
$-103y = -206$

Step3: Solve for y

Isolate $y$ by dividing both sides by -103:
$y = \frac{-206}{-103} = 2$

Step4: Substitute y into first equation

Plug $y=2$ into $-9x -5y = -10$:
$-9x -5(2) = -10$
$-9x -10 = -10$

Step5: Solve for x

Isolate $x$:
$-9x = -10 + 10$
$-9x = 0$
$x = \frac{0}{-9} = 0$

Answer:

$x = 0$
$y = 2$