1. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Step 1.Write both equations in the form Ax + By = C. Step 2.Multiply one or both equations by appropriate numbers so that the sum of the coefficients of either x or y is zero. Step 3.Add the new equations. The sum should be an equation with just one variable. Step 4.Solve the equation from Step 3. Step 5.Substitute the result of Step 4 into either of the given equations and solve for the other variable. Another method of solving a system of equations is by elimination. This method is necessary because later it will be expanded to solve a system of three equations with three unknowns. The Elimination Method Procedure for solving a system of two equations with two unknowns. Step 6.Check the solution in both of the given equations.

2. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Solution: Example 1. Solve the system by elimination: Choose a variable to eliminate. Eliminating x would be easier. Multiply first equation by –1. Add the equations together then solve for y. Next, substitute 1 for y in either equation to obtain the value for the variable x. Then perform the check in both equations. Answer: Solve the system by elimination: Your Turn Problem #1

3. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Solution: Example 2. Solve the system by elimination: Eliminate y by multiplying second row by 5. Add the equations together then solve for x. Next, substitute 5 for x in either equation to obtain the value for the variable y. Then perform the check in both equations. Answer: Solve the system by elimination: Your Turn Problem #2

4. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Solution: Example 3. Solve the system by elimination: Eliminate x by multiplying first row by –2 and second row by 3. Add the equations together then solve for y. Next, substitute 7 for y in either equation to obtain the value for the variable x. Then perform the check in both equations. Answer: Solve the system by elimination: Your Turn Problem #3

5. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Solution: Example 4. Solve the system by elimination: Eliminate x by multiplying first row by –4. Add the equations together then solve for y. Actually both variables cancel and we have 0 = -9 which is not true. Therefore there is no solution. The system is inconsistent with an empty solution set. Answer:  Solve the system by elimination: Your Turn Problem #4 Answer:

6. 9.2 Solving Systems of Linear Equations by Addition BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 Solution: Example 5. Solve the system by elimination: Eliminate x by multiplying first row by 2. Add the equations together then solve for y. Actually both variables cancel and we have 0 = 0 which is true. Therefore there are an infinite number of solutions. The system is dependent. Answer:  To express the solution set, let x = k. The solution set is then: Solve the system by elimination: Your Turn Problem #5 Answer: