Question

solve using elimination. 7x + 9y = -2 -x + y = -18 (\boxed{ }, \boxed{ })

Explanation:

Step1: Multiply the second equation by 7

To eliminate \(x\), we multiply the second equation \(-x + y=-18\) by 7. This gives us:
\(7\times(-x + y)=7\times(-18)\)
\(-7x + 7y=-126\)

Step2: Add the two equations

Now we add the first equation \(7x + 9y=-2\) and the new equation \(-7x + 7y=-126\) together.
\((7x-7x)+(9y + 7y)=-2-126\)
Simplifying the left - hand side and the right - hand side:
\(16y=-128\)

Step3: Solve for y

Divide both sides of the equation \(16y=-128\) by 16:
\(y=\frac{-128}{16}=-8\)

Step4: Substitute y into one of the original equations

We substitute \(y = - 8\) into the second original equation \(-x + y=-18\). So we have:
\(-x-8=-18\)
Add 8 to both sides of the equation:
\(-x=-18 + 8=-10\)
Multiply both sides by - 1 to solve for \(x\):
\(x = 10\)

Answer:

\((10,-8)\)