Question

solve using elimination.
-7x - 8y = -12
-2x - 5y = -17
(□, □)

Explanation:

Step1: Multiply equations to eliminate x

Multiply the first equation by -2 and the second by 7:
$$(-7x - 8y = -12) \times (-2) \Rightarrow 14x + 16y = 24$$
$$(-2x - 5y = -17) \times 7 \Rightarrow -14x - 35y = -119$$

Step2: Add the new equations

Add the two equations to eliminate x:
$$(14x + 16y) + (-14x - 35y) = 24 + (-119)$$
$$14x - 14x + 16y - 35y = 24 - 119$$
$$-19y = -95$$

Step3: Solve for y

Divide both sides by -19:
$$y = \frac{-95}{-19} = 5$$

Step4: Substitute y into an original equation

Substitute \( y = 5 \) into \( -2x - 5y = -17 \):
$$-2x - 5(5) = -17$$
$$-2x - 25 = -17$$

Step5: Solve for x

Add 25 to both sides:
$$-2x = -17 + 25 = 8$$
Divide by -2:
$$x = \frac{8}{-2} = -4$$

Answer:

\((-4, 5)\)