Question

solve the system of equations using the elimination method:

\\
\

$$\begin{aligned} -7x - 8y &= 9 \\\\ -4x + 9y &= -22 \\end{aligned}$$

\\

(7, -1)
(6, 0)
(1, -2)
(0, -2)

Explanation:

Set up the system of equations

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Multiply equations to align coefficients

Using the Elimination Method knowledge point

$$
LATEXBLOCK1
$$

Add the equations to eliminate x

Using the Elimination Method knowledge point

$$
LATEXBLOCK2
$$

Substitute y back to solve for x

Using the Linear Equations knowledge point

$$
LATEXBLOCK3
$$

Verify the solution

Using the Linear Equations knowledge point

$$
LATEXBLOCK4
$$

Answer:

• (A) \((7, -1)\)
• (B) \((6, 0)\)
• (C) \((1, -2)\) (Correct answer)
• (D) \((0, -2)\)