Question

solve the following system of equations.\\(-5x - 3y = -18\\)\\(-7x + 9y = -12\\)\\(x = \square\\)\\(y = \square\\)

Explanation:

Step1: Eliminate y via scaling Eq1

Multiply first equation by 3:
$$3(-5x - 3y) = 3(-18) \implies -15x - 9y = -54$$

Step2: Add to Eq2 to solve for x

Add scaled Eq1 to second equation:
$$(-15x - 9y) + (-7x + 9y) = -54 + (-12)$$
$$-22x = -66 \implies x = \frac{-66}{-22} = 3$$

Step3: Substitute x into Eq1 for y

Plug $x=3$ into $-5x - 3y = -18$:
$$-5(3) - 3y = -18 \implies -15 - 3y = -18$$

Step4: Isolate and solve for y

Rearrange and solve for y:
$$-3y = -18 + 15 \implies -3y = -3 \implies y = \frac{-3}{-3} = 1$$

Answer:

$x = 3$
$y = 1$