Question

8x - 6y = 8\
-4x + 2y = -12

Explanation:

Step1: Multiply the second equation

To eliminate \(x\), multiply the second equation \(-4x + 2y = -12\) by 2. We get \(2\times(-4x + 2y)=2\times(-12)\), which simplifies to \(-8x + 4y = -24\).

Step2: Add the two equations

Now add the first equation \(8x - 6y = 8\) and the new second equation \(-8x + 4y = -24\). \((8x - 6y)+(-8x + 4y)=8+(-24)\). The \(8x\) and \(-8x\) cancel out, leaving \(-2y = -16\).

Step3: Solve for \(y\)

Divide both sides of \(-2y = -16\) by \(-2\). So \(y=\frac{-16}{-2}=8\).

Step4: Substitute \(y\) into an equation

Substitute \(y = 8\) into the second original equation \(-4x + 2y = -12\). We get \(-4x+2\times8=-12\), which simplifies to \(-4x + 16 = -12\).

Step5: Solve for \(x\)

Subtract 16 from both sides: \(-4x=-12 - 16=-28\). Then divide by \(-4\): \(x=\frac{-28}{-4}=7\).

Answer:

\(x = 7\), \(y = 8\)