Solve the simultaneous equations: 3x + 4y = 5 and 2x – 3y = 9

To solve a simultaneous equation we use a method known as elimination. We choose to 'eliminate' or remove the X or Y term. To 'eliminate' x we must firstly determine the lowest common multiple 3 and 2 (as these are the values in front of x in both equations). The lowest common multiple is 6. Therefore, we multiple the first equation by 2 and the second by 3. This gives: 6x + 8y = 10 and 6x - 9y = 27. To 'eliminate' x when can then subtract the second equation from the first. This give us: 17y=-17. Thus, y = -1. We can then substitute y = -1 into the first equation such that 3x+4=5. Rearranging this equation gives, 3x=9. Hence x=9/3=3. Therefore, x=3 and y=-1.