how would you solve the simultaneous equations 3x + 4y = 11, 5x - y = 3?

the first thing to do when trying to solve simultaneous equations like this one is to look for a common coefficient. one of these doesn't exist in the equations as they are so you have to multiply one or both of the equations to find one. In this case you only need to multiply the second equation by 4 to find a common coefficient between the y terms. 20x - 4y = 12, 3x + 4y = 11. now since the common coefficients are of opposite signs you add both sides of the two equations together to give 23x = 23. You can then see that x = 1 and substitute it back into either of the starting equations. 3*1 + 4y = 11, y = 2. You then have the answer to the question x = 1, y = 2.