Question

-9x - 4y = 18
-2x - 3y = -15
(□, □)
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Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 3: \(3(-9x - 4y)=3\times18\) → \(-27x - 12y = 54\)
Multiply the second equation by 4: \(4(-2x - 3y)=4\times(-15)\) → \(-8x - 12y = -60\)

Step2: Subtract the two new equations

\((-27x - 12y)-(-8x - 12y)=54 - (-60)\)
Simplify: \(-27x - 12y + 8x + 12y = 54 + 60\) → \(-19x = 114\)

Step3: Solve for x

\(x=\frac{114}{-19}=-6\)

Step4: Substitute x into one equation (e.g., second equation)

\(-2(-6)-3y=-15\) → \(12 - 3y = -15\)
Subtract 12: \(-3y=-15 - 12=-27\)
Solve for y: \(y=\frac{-27}{-3}=9\)

Answer:

\((-6, 9)\)