Solve the simultaneous equation: 4x-11y=34 and 2x+6y=-6

When solving a simultaneous equation, we will use the elimination method. This method sees us removing or ‘eliminating’ the x or y term. First we need to find the lowest common multiple of the x and y terms from both equations, so it is 4 for the x term, and 66 for the y term. We will choose to eliminate x as this has the lowest common multiple of 4. Hence, we must multiply the second equation by 2, so both x values are 4. This gives us 4x-11y=34 and 4x+12y=-12. To remove the x value, we can subtract the first equation from the second. This leaves us 23y=-46, y=-46/23, thus y=-2. If we then substitute this value into the first equation, we get 4x+22=34. 4x=12, so x=12/4 leaving x=3