Question

1. solve the following system of equations using the elimination method.

$x - y = 11$
$2x + y = 19$

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( x - y = 11 \) and \( 2x + y = 19 \) together.
\( (x - y) + (2x + y) = 11 + 19 \)
Simplifying the left side: \( x - y + 2x + y = 3x \)
Simplifying the right side: \( 11 + 19 = 30 \)
So we get \( 3x = 30 \).

Step2: Solve for \( x \)

Divide both sides of \( 3x = 30 \) by 3.
\( x=\frac{30}{3}=10 \)

Step3: Substitute \( x = 10 \) into one of the original equations to find \( y \)

We'll use the first equation \( x - y = 11 \). Substitute \( x = 10 \):
\( 10 - y = 11 \)
Subtract 10 from both sides: \( -y = 11 - 10 = 1 \)
Multiply both sides by -1: \( y=- 1 \)

Answer:

The solution to the system of equations is \( x = 10 \) and \( y=-1 \).