Solving Linear Systems by Elimination Math Tech II Everette Keller

Two of more linear equations in the same variable form a system of linear equations, or simply a linear system.

y = 3x y = x + 4

To eliminate: To get rid of; remove. To remove (an unknown quantity) by combining equations.

The elimination method can be obtained by (1) multiplying one or both equations by a constant if necessary and (2) adding the resulting equations to eliminate one of the variables

Solve by elimination: Just add the equations 4x + 3y = 16 2x – 3y = 8

Solve by elimination: Multiply First, Then Add 2x + 3y = 3 4x – 6y = 4

Step 1 – Arrange the equations with like terms in columns Step 2 – Multiply, if necessary, the equations by numbers to obtain coefficients that are opposites for one of the variables Step 3 – Add the equations from Step 2. Combining like terms with opposite coefficients will eliminate one variable. Solve for the remaining variable. Step 4 – Substitute the value obtained in Step 3 into either of the original equations and solve for the other variable Step 5 – Check the solution in each of the original equations

Find the solution to the linear system by elimination 5x + 2y = -4 -5x + 3y = 19

Find the solution to the linear system by elimination 3x + 5y = 6 -4x + 2y = 5

1.What does elimination mean in the definitive sense? 2.What does elimination mean for us when working with linear systems? 3.What does the solution that we find through elimination mean? 4.When is it easier to solve by elimination? 5.When is it difficult to solve by this method?

What are the benefits and limitations of solving linear systems through elimination?

Find a real life problem that relates to solving linear systems by elimination and state it for the next class period Problems 1 – 10 on the Handout