Solving Systems of Linear Equations by Graphing
Solve systems of linear equations by graphing both lines and finding their intersection point. Understand consistent and inconsistent systems in Grade 9.
Key Concepts
New Concept A system of linear equations consists of two or more linear equations containing two or more variables. What’s next Next, you’ll graph these equations on a coordinate plane to visually find the one point that solves the entire system.
Common Questions
How do you solve a system by graphing?
Graph both equations on the same coordinate plane. The solution is the intersection point (x,y). Parallel lines mean no solution; same line means infinite solutions.
What does it mean when two graphed lines are parallel?
Parallel lines never intersect, so the system has no solution. It is inconsistent and represents contradictory conditions that cannot both be true.
How does graphing reveal a system with infinite solutions?
When both equations graph as the same line, every point is a solution. This dependent system occurs when one equation is a multiple of the other.