Question

solve.
-8x + 6y = 12
-5x + y = -9

Explanation:

Step1: Solve the second equation for y

From \(-5x + y = -9\), we can express \(y\) in terms of \(x\) by adding \(5x\) to both sides.
\(y = 5x - 9\)

Step2: Substitute y into the first equation

Substitute \(y = 5x - 9\) into \(-8x + 6y = 12\).
\(-8x + 6(5x - 9) = 12\)

Step3: Simplify and solve for x

First, distribute the 6: \(-8x + 30x - 54 = 12\)
Combine like terms: \(22x - 54 = 12\)
Add 54 to both sides: \(22x = 12 + 54\)
\(22x = 66\)
Divide both sides by 22: \(x = \frac{66}{22} = 3\)

Step4: Substitute x back to find y

Substitute \(x = 3\) into \(y = 5x - 9\).
\(y = 5(3) - 9 = 15 - 9 = 6\)

Answer:

\((3, 6)\)