Solving Linear Systems using Linear Combinations (Addition Method) Goal: To solve a system of linear equations using linear combinations

Linear Combination Method 1.Arrange the equations so that like terms are lined up in columns. 2.Look at both equations to see if any like terms are opposites of each other. a)If so, simply add the 2 equations together. b)If not, multiply one or both equations by a real number so that when the equations are added together one variable will cancel out. 3.Solve for the remaining variable. 4.Substitute the value from step 3 into one of the original equations and solve for the other variable. 5.Write the solution as an ordered pair (x,y). 6.Check the solution in each equation of the system.

Example #1Solve using linear combinations. y terms are already opposites…so we can just add Solve for x Now, plug x into one of the equations and solve for y. (4, 0) is the solution. Check (4, 0) in both equations on your paper.

Your Turn Solve using linear combinations. One of the equations needs to be rearranged so that the like terms line up. Now, plug y into one of the equations and solve for x. (1, 2) is the solution. Check (1, 2) in both equations on your paper.

Example #2Solve using linear combinations. No terms are opposites…so we must multiply to make opposites (1, -2) is the solution. -3 * 2 = -6

Example #3Solve using linear combinations. No terms are opposites…so we must multiply to make opposites 3 * 4 = 12