How to solve the simultaneous equations of 3x + 2y = 9 and x-y = 3
First off we can refer to the equations as equation 1 and equation 2. In order to solve the equations we must find a way to combine them that elimates one of the variables ( X or y) so that the other can be found. This value will then be substituted back into either of the original equations so that the second value can be found. In this particular example it is easiest to multiply equation 2 by 2 so that we get an equation of 2x - 2y = 6. In this new version of equation 2 you can see that there is a value of 2y which matches the y value (2y) in equation 1. We will use the new equation to eliminate the y value from equation 1 by adding it to equation 1. 3x + 2y + (2x - 2y) = 9 + 6. This may be simplified to 3x + 2x = 15 so that 5x = 15 and x = 3. We now substitute this x value into one of the original equations to find the y value. 3(3) + 2y = 9, 9 + 2y = 9, 2y = 0 so y = 0. x = 3 and y = 0 is the solution to these simultaneous equations.
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