Question

solve the following system of equations.
-2x + y = 11
5x + y = -17
x =

y =

Explanation:

Step1: Subtract the two equations

We have the system:
\(-2x + y = 11\) (Equation 1)
\(5x + y = -17\) (Equation 2)

Subtract Equation 1 from Equation 2 to eliminate \(y\):
\((5x + y) - (-2x + y) = -17 - 11\)
Simplify the left side: \(5x + y + 2x - y = 7x\)
Simplify the right side: \(-28\)
So, \(7x = -28\)

Step2: Solve for \(x\)

Divide both sides of \(7x = -28\) by 7:
\(x = \frac{-28}{7} = -4\)

Step3: Substitute \(x\) into Equation 1 to find \(y\)

Substitute \(x = -4\) into \(-2x + y = 11\):
\(-2(-4) + y = 11\)
Simplify: \(8 + y = 11\)
Subtract 8 from both sides: \(y = 11 - 8 = 3\)

Answer:

\(x = -4\), \(y = 3\)