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Method

Solving a System of Linear Equations Graphically

Solving a system of linear equations graphically means graphing the lines represented by the equations of the system and identifying the point of intersection. Consider an example system of equations.
To solve the system of equations, three steps must be followed.
1
Write the Equations in Slope-Intercept Form
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Start by writing the equations in slope-intercept form by isolating the variables. For the first linear equation, divide both sides by For the second equation, add to both sides.
Solve for
Solve for
2
Graph the Lines
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Now that the equations are both written in slope-intercept form, they can be graphed on the same coordinate plane.

Graphs of two lines using the slopes and y-intercepts
3
Identify the Point of Intersection
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The point where the lines intersect is the solution to the system.

Point of intersection

The lines appear to intersect at Therefore, this is the solution to the system — the value of is and the value of is

Sometimes the point of intersection of the lines is not a lattice point. In this case, the solution found by solving the system of equations graphically is approximate.