BRIE'

How do you solve systems of equations? There are 3 ways: substitution, combination, and graphing. This web page will show you how to solve an equation for each different way and provide links to other sites for additional help.
SUBSTITUTION: (Equation 1) 3x + 4y = -4 (Equation 2) x + 2y = 2 * First solve for one variable for one equation. In this example, solve for 'x' and you will have x = -2y + 2. * Next, plug in the 'x' value from equation 2 into equation 1. You should now have 3(-2y + 2) + 4y = -4. * Then solve the equation and the answer is y = 5. * After getting 'y', plug in 5 for 'y' in the revised equation 1. You should now have x = -2 (5) + 2. * Finally, solve for 'x' and you should get x = -8. * The solution is (-8, 5).	GRAPHING: * When graphing a linear equation, the solution will be either no solution ( parallel lines), infinite solutions ( the same line), or one solution ( intersecting lines at only one point). * Example: You are on the prom committee and in charge of buying balloons. You want to use both latex and mylar balloons. Latex balloons cost $.10 each and mylar balloons cost $.50 each. You need 125 balloons and you have $32.50 to spend. How many of each balloon can you buy? * To solve this, first write the two equations which are: x + y =125 and .1x + .5y = 32.50. Next, graph the two equations and find the intersecting point. That point is the solution. The solution is (75, 50) so your answer is 75 latex balloons and 50 mylar balloons.
COMBINATION: (Equation 1) 3x + 4y = -3 (Equation 2) 2x + y = 8 * First multiply one or both of the equations by a constant to get coefficients that only differ in sign for one of the variables. For this equation, multiply equation 2 by -4. Equation 2 should now be -8x - 4y = -32. * Next, add the equations together and solve for 'x' since the 'y' was cancelled out. x = 7. * Now, plug in the 'x' value and solve for 'y'. y = -6. So your solution will be ( 7, -6).