Question

-3x - 4y = 2
6x + 6y = -6

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), we multiply the first equation \(-3x - 4y = 2\) by 2.
\(2\times(-3x - 4y)=2\times2\)
\(-6x - 8y = 4\)

Step2: Add to second equation

Now add the new first equation \(-6x - 8y = 4\) to the second equation \(6x + 6y = -6\).
\((-6x - 8y)+(6x + 6y)=4+(-6)\)
Simplify: \(-2y = -2\)

Step3: Solve for \(y\)

Divide both sides by \(-2\):
\(y=\frac{-2}{-2}=1\)

Step4: Substitute \(y\) into second equation

Substitute \(y = 1\) into \(6x + 6y = -6\):
\(6x + 6\times1 = -6\)
\(6x + 6 = -6\)

Step5: Solve for \(x\)

Subtract 6 from both sides:
\(6x = -6 - 6=-12\)
Divide by 6:
\(x=\frac{-12}{6}=-2\)

Answer:

\(x = -2\), \(y = 1\)