Question

question 8
solve the system of equations using elimination. (fill each blank with an integer.)
$-x + y = 10$
$-2x + 8y = -16$
$(square, square)$

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by -2:
$$-2(-x + y) = -2(10) \implies 2x - 2y = -20$$

Step2: Add to second equation

Add new equation to $-2x + 8y = -16$:
$$(2x - 2y) + (-2x + 8y) = -20 + (-16)$$
$$6y = -36$$

Step3: Solve for $y$

Divide both sides by 6:
$$y = \frac{-36}{6} = -6$$

Step4: Substitute $y$ to find $x$

Plug $y=-6$ into $-x + y = 10$:
$$-x + (-6) = 10 \implies -x = 16 \implies x = -16$$

Answer:

$(-16, -6)$