Master

Solving Systems of Linear Equations using Graphing

Master solving systems of linear equations using graphing with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Solving Systems of Linear Equations using Graphing

Study Guide

Key Definition

A system of linear equations is a set of two or more linear equations. In two variables ( $x$ and $y$), the graph of a system of two equations is a pair of lines in the plane.

Important Notes

The lines intersect at zero points if they are parallel.
The lines intersect at exactly one point in most cases.
The lines intersect at infinitely many points if they represent the same line.
Graphing is useful for rough answers or when intersections are at integer coordinates.
Use slope-intercept form to graph lines easily.

Mathematical Notation

$y = mx + b$ is the slope-intercept form of a line

$m$ is the slope of the line

$b$ is the y-intercept

Remember to use proper notation when solving problems

Why It Works

Graphing shows the visual intersection of the lines, which is the solution to the system.

Remember

The intersection point is the solution, represented by $(x, y)$.

Quick Reference

Slope-Intercept Form:$y = mx + b$

Understanding Solving Systems of Linear Equations using Graphing

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When solving by graphing, rewrite each equation in slope-intercept form $y = mx + b$. Identify the slope $m$ and y-intercept $b$ for each line. On a coordinate plane, plot the y-intercept point at $(0, b)$, then use the slope $m$ to locate a second point (rise over run). Draw the line through these points. Repeat for the second equation. The point where the two lines cross is the solution $(x, y)$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the slope of the line given by $y = 0.5x + 2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are plotting the growth of savings over time, represented by $y = 0.5x + 2$. What does the slope represent?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the equation $y = -2x - 3$. What does the y-intercept represent?

Challenge Quiz

Single Choice Quiz

Advanced

Where do the lines $y = 0.5x + 2$ and $y = -2x - 3$ intersect?

Recap

Watch & Learn

Review key concepts and takeaways