Lesson 13 3 Systems of Equations Objective By

Lesson 13. 3 Systems of Equations Objective: By the end of this lesson you will be able to solve systems of equations using the substitution or elimination methods.

What is a system of equations? System of Equations: Two or more equations graphed on the same coordinate axes. When two linear equations are graphed on the same coordinate plane, there are three possible outcomes. The lines may be parallel: no solution The lines may intersect: one solution The lines may coincide (lie right on top of each other): infinite solution The point where the lines intersect is the “solution” to the system.

2 Methods to Solve a System The first method of solving a system that we will cover is the substitution method. Find the intersection of the two lines corresponding to x = 4 and y = 2 x + 8. Substitute one equation into the other equation. Therefore, the point where the lines intersect would be (4, 16)

Elimination method Find the intersection of the lines corresponding to the following system. 8 x – 3 y = 7 10 x + 4 y = 1 To use the elimination method you may multiply either equation by whatever number you’d like, as long as after adding the two equations together, one of the variables cancels out.

Now substitute ½ for x in either equation to find y. Then the solution is: (1/2, 1)

Find the intersection of the lines corresponding to the following system. y = 3 x + 1 6 x – 2 y = -2 Since the statement -2 = -2 is a true statement, the graphs intersect everywhere, have infinite solutions, or are a coinciding system.

Summary When is substitution method easier than elimination method? When is elimination easier? Homework: w/s 13. 3