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

When solving simultaneous equations there are several options, the two most common methods being substitution and elimination. For this example I shall use elimination. In order to do so, either x or y must have the same coefficient in both equations. The simplest way of doing so is to multiply the second equation by 2 in order that the coefficient of y in both equations is 2. This gives us 4x+2y=6. We can then subtract the second equation from the first to eliminate y as a variable. This leaves -x=-2 or more simply put, x=2. We then substitute x=2 into either equation to solve for y. If we use the first we get: 3(2)+2y=4 or 6+2y=4. To simplify this, we take 6 over to the right side and subtract it from 4 (since signs become the opposite when taken over the equals sign). We are left with: 2y=-2. We divide both sides by 2 and are left with y=-1.