Lesson 7-3 Solving Linear Systems of Equations using Elimination

What does Elimination mean? You can use the Properties of Equality to solve a system of equations using elimination If a = b and c = d Then a+c = b+d (adding the same amount to both sides, still true) and also a – c = b –d (subtracting the same amount to both sides, still true)

Adding Equations: Example 1 If in a system of equations, both equations have the same but opposite sign coefficients for x or y, you can add the equations together to eliminate one of the variables. STEPS 1.Add the equations together to eliminate one variable 2.Solve for the remaining variable 3.Solve for the eliminated variable, using either of the original equations

Your Turn

Subtracting Equations: Example 1 If in a system of equations, both equations have the same coefficients for x or y, you can subtract the equations together to eliminate one of the variables. STEPS 1.Add/subtract the equations together to eliminate one variable 2.Solve for the remaining variable 3.Solve for the eliminated variable, using either of the original equations

A Quick Way to Subtract Equations

Your Turn Solve by elimination. 1.x + 5y = 9 x - y = x - 2y = 15 2x - 2y = 3

Multiplying One Equation: Example 2 To eliminate a variable, the coefficient, both equations have the same or opposite sign coefficients for x or y. You may need to add a step, and multiply one of the equations by a constant first. Think: Is the x or y set of variables a simple multiple of the other? What could I multiply the first equation by to be able to eliminate the x term when I add/subtract the two equations together?

Solve by Elimination STEPS 1.Multiply one of the equations by a number that will enable elimination of one of the variables 2.Add/subtract the equations together to eliminate one variable 3.Solve for the remaining variable 4.Solve for the eliminated variable, using either of the original equations

To Be Continued…

Your Turn 1) 3)

Assignment

Multiplying Both Equations To eliminate a variable, you may need to multiply both equations by a (non-zero) constant. Multiply each equation by a number that will allow you to eliminate a variable when you add or subtract the equations together. STEPS 1.Multiply both of the equations by a number that will enable elimination of one of the variables 2.Add/subtract the equations together to eliminate one variable 3.Solve for the remaining variable 4.Solve for the eliminated variable, using either of the original equations Think: What could I multiply each equation by to be able to eliminate the x term when I add/subtract the two equations together?

Assignment