Question

solve using elimination.\
-9x - 10y = 9\
-9x - 7y = -18\
(\square, \square)

Explanation:

Step1: Subtract the two equations

To eliminate \(x\), we subtract the second equation from the first equation. Let the first equation be \( -9x - 10y = 9\) and the second be \( -9x - 7y = -18\). Subtracting the second from the first: \((-9x - 10y)-(-9x - 7y)=9 - (-18)\)
Simplify left side: \(-9x - 10y + 9x + 7y=-3y\)
Right side: \(9 + 18 = 27\)
So we have \(-3y = 27\)

Step2: Solve for y

Divide both sides by \(-3\): \(y=\frac{27}{-3}=-9\)

Step3: Substitute y into one equation to find x

Use the first equation \(-9x - 10y = 9\). Substitute \(y = -9\): \(-9x - 10(-9)=9\)
Simplify: \(-9x + 90 = 9\)
Subtract 90 from both sides: \(-9x=9 - 90=-81\)
Divide by \(-9\): \(x=\frac{-81}{-9}=9\)

Answer:

\((9, -9)\)