Step 1. Write each equation in slope-intercept form. (y=mx+b)

Step 2. Graph each equation on the same set of axes. Get the coordinates of the point where the lines intersect if it exists. (They will not intersect if the lines are parallel!)

Step 3. Check the result by plugging the coordinates into both equations. The coordinates must satisfy BOTH equations.

Examples Done by Reade Vaisman

Directions: Solve the linear system graphically.

y – x = 3

y + 2x = -3

Step 1. Put the equations in y = mx + b

	y – x = 3			y + 2x = -3
Add x to both sides.	y=x+3			y=-2x-3	Subtract 2x from both sides.

Step 2. Graph the equations and find the point of intersection.

Step 3. Check the result by plugging the coordinates (-2,1) into both equations. The coordinates must satisfy BOTH equations.

y-x=3		y + 2x = -3
1-(-2)=3?		1+2(-2)=-3?
1+2=3?		1-4=-3?
3 = 3		-3=-3
yes		yes

Problems You Should Try

Directions: Please solve the following linear systems using the graphical method. If there is no solution to the linear system, indicate so by stating "null set". (Click here for graph paper.)