Solve by the linear combination method (with or without multiplication) 6x-2y=2 -3x+4y=5

6x - 2y = 2
-3x + 4y =5

Multiplying the second equation by 2 yields:
-6x + 8y = 10

Adding the first equation and this new second equations yields

6x-2y=2
-6x+8y=10

6y = 12, y = 2.
substituting back into one of the original equations yields
6x - 2(2) = 2, 6x - 4 = 2, 6x = 6, x = 1

Double check x=1 and y = 2:

6(1) - 2(2) = 2, 6 -4 = 2, 2 =2
-3(1) + 4(2) = 5, -3 + 8 = 5, 5=5.

Solved. x = 1, y = 2.