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← Solving Systems of Equations by Graphing

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. 2y=- 2x+8 x=y-1 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 y-variables. For the first linear equation, divide both sides by 2. For the second equation, add 1 to both sides.

2y=- 2x+8 & (I) x=y-1 & (II)
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(I): Solve for y
DivEqn

(I): .LHS /2.=.RHS /2.

y= - 2x+82 x=y-1
WriteSumFrac

(I): Write as a sum of fractions

y= - 2x2+ 82 x=y-1
MovePartNumRight

(I): a* b/c=a/c* b

y= - 22x+ 82 x=y-1
MoveNegNumToFrac

(I): Put minus sign in front of fraction

y=- 22x+ 82 x=y-1
CalcQuot

(I): Calculate quotient

y=- 1x+4 x=y-1
IdPropMult

(I): Identity Property of Multiplication

y=- x+4 x=y-1
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(II): Solve for y
AddEqn

(II): LHS+1=RHS+1

y=- x+4 x+1=y
RearrangeEqn

(II): Rearrange equation

y=- x+4 y=x+1

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 (1.5,2.5). Therefore, this is the solution to the system — the value of x is 1.5 and the value of y is 2.5.

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.

Exercises

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