We can solve this system of equations using the **elimination method**. The given system is:

1. \( x - y = 2 \)
2. \( -2x + 2y = 2 \)

### Step 1: Add the equations to eliminate one variable.

First, observe that adding the two equations will eliminate the \( y \)-terms since their coefficients are opposites.

\[
(x - y) + (-2x + 2y) = 2 + 2
\]

Simplifying both sides:

\[
x - y - 2x + 2y = 4
\]
\[
- x + y = 4
\]

### Step 2: Substitute or simplify further.

The resulting equation is \( -x + y = 4 \). However, this doesn't directly eliminate a variable, so we could revisit the first equation to try a simpler strategy:

Multiplying

solve for elimination x - y = 2, -2x + 2y = 2

Learn how to solve the system of linear equations x - y = 2 and -2x + 2y = 2 using the elimination method. This step-by-step guide explains the process of eliminating variables and simplifying the solution. Suitable for students in Grades 8-10.

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