Solving Systems of Equations by Graphing
Solve systems of equations by graphing in Grade 10 algebra. Convert equations to slope-intercept form, plot both lines, and identify the intersection as the solution to the linear system.
Key Concepts
New Concept A system of equations is a collection of two or more equations containing two or more of the same variables.
What’s next Next, you’ll learn the most visual way to find a solution: graphing the equations to see where they intersect.
Common Questions
How do you solve a system of linear equations by graphing?
Rewrite both equations in y = mx + b form. Graph both on the same axes using slope and y-intercept. The solution is the coordinates of the intersection point.
What are the three possible outcomes when solving a system by graphing?
Two intersecting lines: one solution (the intersection point). Parallel lines: no solution. Coincident lines (same line): infinitely many solutions.
How accurate is the graphing method for solving systems?
Graphing provides a visual solution but can be imprecise for non-integer answers. Use algebraic methods (substitution or elimination) to verify or get exact solutions.