Q: How to solve the simultaneous equations 3x+2y=7 and 5x+y=14

When solving simultaneous equations you are aiming to use both equations together to find out the value of x and y for values that with ‘fit’ in each equation.

3x + 2y = 7

5x + y = 14

If we subtract these equations from each other in a way that we end up eliminating y, when can find the value of x. The way we do this is to multiply equation 2 by 2, remembering to multiply both sides of the equation. This gives

2. 10x + 2y = 28

Now, when we subtract equation 1 from equation 2 we get

(10x – 3x) + (2y - 2y) = 28 – 7

7x = 21

x = 3

Now we have found the value of x we can substitute it back into equation 1 to find the value of y.

3x + 2y = 7 and x = 3

9 + 2y = 7

2y = -2

y = -1