Question

1. 8x - 6y = -20

-16x + 7y = 30

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), we multiply the first equation \(8x - 6y = -20\) by 2.
\(2\times(8x - 6y)=2\times(-20)\)
\(16x - 12y = -40\)

Step2: Add new equation to second equation

Now add the new equation \(16x - 12y = -40\) to the second equation \(-16x + 7y = 30\).
\((16x - 12y)+(-16x + 7y)=-40 + 30\)
Simplify left side: \(16x - 16x - 12y + 7y=-5y\)
Right side: \(-10\)
So, \(-5y=-10\)

Step3: Solve for \(y\)

Divide both sides by \(-5\):
\(y=\frac{-10}{-5}=2\)

Step4: Substitute \(y = 2\) into first equation

Substitute \(y = 2\) into \(8x - 6y = -20\):
\(8x - 6\times2=-20\)
\(8x - 12=-20\)

Step5: Solve for \(x\)

Add 12 to both sides:
\(8x=-20 + 12=-8\)
Divide by 8:
\(x=\frac{-8}{8}=-1\)

Answer:

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