Solving Linear Systems by Graphing
A system of equations is a set of two or more equations with the same variables. In this chapter we will focus on the system consisting of two equations in two unknowns. The solution of such system is an ordered pair that satisfies both equations.
There are three ways to solve systems of linear equations in two variables:
- Graphing method
- Substitution method
- Elimination method
Step 1: Graph the first equation.
Step 2: Graph the second equation on the same coordinate system as the first.
Step 3: Find the coordinates of the point of intersection of the two lines which is the solution of the system
Step 4: Substitute the values in the two equations and check if the solution is valid.
If it makes BOTH equations true then you have your solution to the system.
If it makes at least one of them false, you need to go back and redo the problem.
Remark:
- If two lines intersect at one place, then the point of intersection is the solution to the system.
- If the two lines are parallel, then they never intersect, so there is no solution.
- If the two lines lie on top of each other, then they are the same line and you have an infinite number of solutions.
Solving Linear Systems by Graphing
Practice: Solve systems of equations by graphing in the following exercises.