Question

1. $x + 2y = 13$

$-x + y = 5$

Explanation:

Step1: Define the system of equations

We have the system:

$$\begin{cases} x + 2y = 13 \\ -x + y = 5 \end{cases}$$

Step2: Add the two equations

Adding the left - hand sides and the right - hand sides of the two equations to eliminate \(x\):
\((x + 2y)+(-x + y)=13 + 5\)
Simplify the left - hand side: \(x+2y - x + y=3y\), and the right - hand side: \(18\). So we get \(3y=18\).

Step3: Solve for y

Divide both sides of the equation \(3y = 18\) by 3: \(y=\frac{18}{3}=6\).

Step4: Substitute y into one of the equations to solve for x

Substitute \(y = 6\) into the second equation \(-x + y=5\), we have \(-x+6 = 5\).
Subtract 6 from both sides: \(-x=5 - 6=-1\).
Multiply both sides by - 1: \(x = 1\).

Answer:

The solution to the system of equations is \(x = 1\) and \(y=6\)