For that one, there's no way to get an equivalent term by changing just one of them (without involving fractions), so you need to change both.

2x - 3y = 2 --> 6x - 9y = 6

3x + 2y = 16 --> 6x + 4y = 32

Take the first from the second:

13y = 26 ∴ y = 2

Substitute in y = 2: 2x - (3*2) = 2, 2x = 8, x = 4

Check: 3*4 + 2*2 = 16.

**x = 4, y = 2**

You always use the method of making variables match when the two equations are linear. If they are quadratic, you need to use substitution.

The way to use substitution for the example above would be to rearrange the first equation to give x as the subject:

2x - 3y = 2

2x = 2 + 3y

x = (2 + 3y)/2

Then substitute that into the second equation.

3[(2 + 3y)/2] +2y = 16

That can be used to solve for y and then you would go back and use the y value to find x, as before.