Hi Conor,

If the second equation were just 5y = 4x you could add the equations and get

7x - 5y + 5y = -1 + 4x
7x = -1 + 4x

and solve for x. Unfortunately the second equation is 3y = 4, but with a little care you can use the same technique. Look at your equations again

7x - 5y = -1
3y = 4x

If you multiple both sides of the first equation by 3 and both sides of the second equation by 5 then the y term in the first equation becomes -15y and the y term in the second equation becomes 15y. Now you can add the two equations and the y terms cancel. So here is my solution.

Multiply both sides of the first equation by 3 and both sides of the second equation by 5 to get

21x - 15y = -3
15y = 20x

Add the two equations

21x - 15y + 15y = -3 + 20x
21x = -3 + 20x

Solve for x. Once you know x you can substitute its value into your second equation, 3y = 4x to find y.

Penny