How do I solve an equation with both x and y variables (simultaneous equation)?

A simultaneous equation is calculated to find the pair of co-ordinates where two straight lines cross on a graph, so the question you've probably been asked is to 'solve' a pair of linear equations. This might look like: Solve the simultaneous equations: 2x + y = 5 and 3x + y = 7. The key is to answer this question in 3 steps: Eliminate, Substitute and Check. First, you want to 'eliminate' one of the variables temporarily and make sure only one variable remains, so start by subtracting common factors - in this case the 'y'. E.g. (3x + y = 7) - (2x + y = 5) --> x = 2. Once you have the x value, 'substitute' it into Equation 1 and find the value of the y variable. E.g. (3x + y = 7) --> (3(2) + y = 7) --> (6 + y = 7) --> y = 1. Finally, 'check' your answers by substituting both numbers into Equation 2. If the numbers add up correctly, then you're right and have lost no marks! E.g. (2x + y = 5) --> 2(2) + 1 = 5