How do I solve the linear system by elimination?

X-2y=-6

3x-2y=2

x-2y=-6

Solving for x.

Add 2y to both sides.

x-2y+2y=-6+2y

x=2y-6.

x-2y=-6

Add - x to both sides.

x-2y+-x=-6+-x

-2y=-x-6

Solving for y.

Step 2: Divide both sides by - 2.

-2y-2=-x-6-2

y=1/2x+3

3x-2y=2

Solving for x.

Add 2y to both sides.

3x-2y+2y=2+2y

3x=2y+2

Divide both sides by 3.

3x/3 = 2y+2/3

x=2/3y+2/3

3x-2y=2

Solving for y.

Add - 3x to both sides.

3x-2y+-3x=2+-3x

-2y=-3x+2

Divide both sides by - 2.

-2y/-2 = - 3x+2/-2

y=3/2x-1