Question

x + y = -11
-4x + y = 5

Explanation:

Step1: Subtract the first equation from the second equation to eliminate \( y \)

We have the system of equations:
\[

$$\begin{cases} x + y = -11 \quad (1)\\ -4x + y = 5 \quad (2) \end{cases}$$

\]
Subtract equation \((1)\) from equation \((2)\):
\[
(-4x + y) - (x + y) = 5 - (-11)
\]
Simplify the left - hand side: \(-4x + y - x - y=-5x\)
Simplify the right - hand side: \(5 + 11 = 16\)
So we get the equation \(-5x=16\)

Step2: Solve for \( x \)

Divide both sides of the equation \(-5x = 16\) by \(-5\):
\(x=\frac{16}{-5}=-\frac{16}{5}=-3.2\)

Step3: Substitute \( x = -\frac{16}{5} \) into the first equation to solve for \( y \)

Substitute \( x = -\frac{16}{5} \) into \( x + y=-11\):
\(-\frac{16}{5}+y=-11\)
Add \(\frac{16}{5}\) to both sides of the equation:
\(y=-11+\frac{16}{5}\)
First, rewrite \(-11\) as \(-\frac{55}{5}\), then \(y = -\frac{55}{5}+\frac{16}{5}=\frac{-55 + 16}{5}=\frac{-39}{5}=-7.8\)

Answer:

The solution of the system of equations is \(x = -\frac{16}{5},y=-\frac{39}{5}\) (or \(x=-3.2,y = - 7.8\))