How to solve simultaneous equations with two unknowns?

There are two methods for solving simultaneous equations, the algebraic method or graphic method. While using graphs is a useful visual way to solve simultaneous equations, this is more time consuming and should only be done if the exam question asks specifically. Here’s how to use the algebraic method for to solve the two unknowns in the equations: 7x + 2y = 2               2x - 2y = 34 Start by eliminating one of the unknowns: In this example we can do this by adding the two equations to eliminate the y’s:           7x + 2y = 2 2x - 2y = 34 9x = 36 Solve to find the first unknown To find x we need to divide both sides by 9:           9x = 36      x = 4 Substitute this value into one of the original equations to find the second unknown: Substituting x = 4 into one of our original equations to solve y gives: 7(4) + 2y = 2 28 + 2y = 2                subtract 28 from each side to isolate the y factor 2y = - 26                    divide both sides by 2 to solve y           y = - 13         The final step is to check our values x = 4 and y = -13 by substituting them into the second equation: 2x - 2y = 34 2(4) – 2(-13) = 34 8 + 26 = 34 These four steps can be used to solve simultaneous equations with two unknown values.