How Do You Solve a System of Equations by Graphing?

How Do You Solve a System of Equations by Graphing?

Note:

There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by graphing both lines and finding their intersection. Take a look!

Keywords:

  • problem
  • line
  • linear equations
  • system of equations
  • system
  • 2 equations
  • find intersection
  • solve system of equations
  • solve graphically
  • line intersection
  • graph line intersection
  • plot
  • consistent
  • 1 solution
  • independent
  • 2 equations
  • 2 unknowns
  • 2 variables

Background Tutorials

  • Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

      • What's Slope-Intercept Form of a Linear Equation?What's Slope-Intercept Form of a Linear Equation?

      What's Slope-Intercept Form of a Linear Equation?

      When you're learning about linear equations, you're bound to run into the point-slope form of a line. This form is quite useful in creating an equation of a line if you're given the slope and a point on the line. Watch this tutorial, and learn about the point-slope form of a line!

  • Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

      • What's a System of Linear Equations?What's a System of Linear Equations?

      What's a System of Linear Equations?

      A system of equations is a set of equations with the same variables. If the equations are all linear, then you have a system of linear equations! To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This tutorial will introduce you to these systems.

      • What's a Solution to a System of Linear Equations?What's a Solution to a System of Linear Equations?

      What's a Solution to a System of Linear Equations?

      If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time. Follow along as this tutorial uses an example to explain the solution to a system of equations!

Further Exploration

  • Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

      • How Do You Solve a System of Equations Using the Substitution Method?How Do You Solve a System of Equations Using the Substitution Method?

      How Do You Solve a System of Equations Using the Substitution Method?

      There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by substituting one equation into the other and solving for the variable. Then, see how to use that variable value to find the value of the other variable. Check it out!