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Objectives
Solve systems of linear equations in two variables by elimination method.
Use elimination to combine two equations in order to eliminate one variable.
Choose an appropriate method for solving linear systems.
Another method for solving systems of equations is elimination. Just like the substitution method, the goal of elimination is to reduce the system down to one equation that has only one variable. This is accomplished by combining the two equations in the system together in such a way that one of the variables cancels out.
Video Tutorial
Solve a Linear System Using the Elimination Method
The solution for example 1 is shown in the slide show to the right. Hover over the image and use the left and right arrows to follow each step of the solution.
Video Tutorial
Video Tutorial
This video solves the linear system in Ex (2) using the elimination method.
Video Tutorial
Video Tutorial
This video solves the linear system in Ex (3) using the elimination method.
Solve Word Problems by Elimination Method
Problem 1: Suppose you have $42,250 invested in two accounts. The first is a cash deposit earning interest at 7½ percent annually and the second is a federal bond earning interest at 5 percent annually. The combined interest after one year is $2575. How much is invested in each account?
Problem #1 Solution
Problem 2: You and some friends are at a summer concert and grabbed a bunch of hot dogs and hamburgers from the food vendor. Hot dogs cost $2.75 each and Hamburgers cost $3.25 each. If 13 items were tallied for a total cost of $39.75 how many of each did you get?
Problem #2 Solution
Problem 3: A chemist has a bottle of 1% acid solution and a bottle of 5% acid solution. She wants to mix the two solutions to create 100 mL of a 4% acid solution. How much of each solution is needed for this mixture?
Problem #3 Solution
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