Question

solve the following system of equations.
-4x + y = 13
5x + y = -14
x =

y =

Explanation:

Step1: Subtract the two equations to eliminate \( y \)

We have the system:
\[

$$\begin{cases} -4x + y = 13 \\ 5x + y = -14 \end{cases}$$

\]
Subtract the first equation from the second equation:
\((5x + y) - (-4x + y) = -14 - 13\)
Simplify the left side: \(5x + y + 4x - y = 9x\)
Simplify the right side: \(-27\)
So we get \(9x = -27\)

Step2: Solve for \( x \)

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

Step3: Substitute \( x = -3 \) into one of the original equations to find \( y \)

Let's use the first equation \(-4x + y = 13\). Substitute \( x = -3 \):
\(-4(-3) + y = 13\)
Simplify \(-4(-3)\): \(12 + y = 13\)
Subtract 12 from both sides: \(y = 13 - 12 = 1\)

Answer:

\( x = -3 \)
\( y = 1 \)