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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. 2y=- 2x+8 x=y-1 To solve the system of equations, three steps must be followed.

Write the Equations in Slope-Intercept Form

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

Graph the Lines

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

Identify the Point of Intersection

The point where the lines intersect is the solution to the system.

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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