A system of linear equations is a set of linear equations that have common variables. Common systems consist of two variables, x and y, and two linear equations. The solution to the system is the value of x and y that satisfy both equations. There are two ways to solve systems: substitution and elimination. Step 1: Solve one equation in terms of one of the variables whichever is easier. Step 2: Substitute one equation into the other in terms of the variable found in step one.
Homework: Systems of Equations Word Problems Quiz - Quizizz
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If you missed this problem, review Example 1. If you missed this problem, review Example 2. We have solved systems of linear equations by graphing and by substitution. Graphing works well when the variable coefficients are small and the solution has integer values.
There are two methods that will be used in this lesson to solve a system of linear equations algebraically. They are 1 substitution , and 2 elimination. They are both aimed at eliminating one variable so that normal algebraic means can be used to solve for the other variable. Once one variable is solved, then substitution will be used in both above methods to find the second variable. Special Circumstances.