[ 2x - 3y = 7 ] *3 = [ 6x - 9y = 21 ]

[ 3x + 4y = 2 ] *2 = [ 6x + 8y = 4 ]

[ 6x + 8y = 4 ] - [ 6x - 9y = 21 ] = [ 17y = -17 ]

Therefore, y = -1.

Substituting y = -1 into the original equations and solving for x we get the following.

2x + 3 = 7

2x = 4

x = 2

And,

3x - 4 = 2

3x = 6

x = 2

So we have x = 2 and y = -1.