Question

1. \

$$\begin{cases} x - y = 5 \\\\ -x - 3y = 7 \\end{cases}$$

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases} x - y = 5 \\ -x - 3y = 7 \end{cases}$$

Adding the two equations together: \((x - y)+(-x - 3y)=5 + 7\)
Simplify the left - hand side: \(x - y-x - 3y = 5+7\), which simplifies to \(-4y=12\)

Step2: Solve for y

From \(-4y = 12\), divide both sides by \(-4\): \(y=\frac{12}{-4}=- 3\)

Step3: Substitute y into the first equation

Substitute \(y = - 3\) into the equation \(x - y=5\), we get \(x-(-3)=5\), which is \(x + 3=5\)

Step4: Solve for x

Subtract 3 from both sides of \(x + 3=5\): \(x=5 - 3=2\)

Answer:

The solution of the system of equations is \(x = 2,y=-3\)