Question

1. $x - y = 5$ $-3x + y = -1$

Explanation:

Step1: Add the two equations

We have the system of equations:
\[

$$\begin{cases} x - y = 5 \\ -3x + y = -1 \end{cases}$$

\]
Adding the two equations together: \((x - y)+(-3x + y)=5+(-1)\)
Simplify the left - hand side: \(x - y-3x + y=(x - 3x)+(-y + y)=-2x\)
Simplify the right - hand side: \(5+( - 1)=4\)
So we get the equation \(-2x = 4\)

Step2: Solve for x

From \(-2x = 4\), divide both sides by \(-2\): \(x=\frac{4}{-2}=-2\)

Step3: Substitute x into the first equation to solve for y

Substitute \(x = - 2\) into the equation \(x - y=5\), we have \(-2 - y=5\)
Add 2 to both sides of the equation: \(-y=5 + 2=7\)
Multiply both sides by \(-1\): \(y=-7\)

Answer:

The solution to the system of equations is \(x=-2,y = - 7\)