Problem

$\begin{array}{l}3 x+2 y=-18 \\ 2 x+9 y=-12\end{array}$

Answer

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Answer

\(\boxed{x = -6, y = 0}\)

Steps

Step 1 ：Multiply the first equation by 2 and the second equation by 3: \(\begin{cases} 6x + 4y = -36 \\ 6x + 27y = -36 \end{cases}\)

Step 2 ：Subtract the second equation from the first equation to eliminate x: \(-23y = 0\)

Step 3 ：Solve for y: \(y = 0\)

Step 4 ：Substitute the value of y back into one of the original equations to find the value of x: \(3x + 2(0) = -18\)

Step 5 ：Solve for x: \(x = -6\)

Step 6 ：\(\boxed{x = -6, y = 0}\)

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