Question

solve the following system of equations.\\(-5x + 4y = -14\\)\\(-9x - 8y = -10\\)\\(x = \square\\)\\(y = \square\\)

Explanation:

Step1: Eliminate y, multiply first eq by 2

$2(-5x + 4y) = 2(-14) \implies -10x + 8y = -28$

Step2: Add to second equation

$(-10x + 8y) + (-9x - 8y) = -28 + (-10)$
$\implies -19x = -38$

Step3: Solve for x

$x = \frac{-38}{-19} = 2$

Step4: Substitute x=2 into first eq

$-5(2) + 4y = -14 \implies -10 + 4y = -14$

Step5: Solve for y

$4y = -14 + 10 \implies 4y = -4 \implies y = \frac{-4}{4} = -1$

Answer:

$x = 2$
$y = -1$