Solving Systems of Equations Graphically
Standard
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Strategy: Convert to slope-intercept form if needed since these are easier to graph. If the lines intersect, you have a solution.
Example 1
1. y = 2x + 3
2. y = -2x -2
1. Plot the graph like you normally would
- identify the y-int: 3
- identify the slope: 2
2. Plot the graph like you normally would
- identify the y-int: -2
- identify the slope: -2
Hover and click on the the intersection of the two graphs. This is your solution to the system of equations.
The red graph is y = 2x + 3
The blue graph is y = -2x - 2
Example 2
When the equations aren't given in slope-intercept form, you need to convert them and change them to slope intercept form. To do that, you have to solve for y, and then you continue to graph them like you would with slope intercept form.
Our two equations
1. 2x + 3y = 5
2. 6x - 2y = 4
Solve for y
2x + 3y = 5
3y = -2x + 5
y = (-2/3)x + 5/3
6x - 2y = 4
-2y = -6x + 4
y = 3x - 2
Now we have two slope intercept equations that we can easily graph.
1. y = (-2/3)x + 5/3
2. y = 3x -2
1. Plot the graph like you normally would
- identify the y-int: 5/3
- identify the slope: -2/3
2. Plot the graph like you normally would
- identify the y-int: 3
- identify the slope: -2
Hover and click on the intersection of the two graphs to find your solution.
The purple graph is y = 3x - 2
The green graph is y = (-2/3)x + 5/3
External Resource
Solving systems of equations graphically