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5 minutes
Warm-Up
Write each equation in slope-intercept form.
1) x – y = 6
2) 2x = 5y
3) 4x + 5y = 15
4) x = -2
5) y = 3
Method #3
Solving Systems by Graphing
Objectives:
•Solve a system of linear equations in two variables by
graphing
Example 1
Graph and classify each system. Then find
the solution from the graph.
x  y  2

x  y
 y  x  2

y  x
8
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
(1,1)
2
4
6
8
Example 2
Graph and classify each system. Then find
the solution from the graph.
8
x+y=6
2x - y = 6
x+y=6
2x - y = 6
-x
-x
-2x
-2x -8 -6
y = -x + 6 -y = -2x + 6
y = 2x - 6
6
4
(4,2)
2
-4
-2
-2
-4
-6
-8
2
4
6
8
Example 3
Graph and classify each system. Then find
the solution from the graph.
8
x – 3y = -6
x + 2y = -6
x – 3y = -6
-x
-x
-3y = -x – 6
x + 2y = -6
-x
-x
2y = -x – 6
6
(-6,0)
-8 -6
-4
4
2
-2
-2
-4
y = 1/3 x + 2 y = -1/2 x - 3
-6
-8
2
4
6
8
Example 4
Graph and classify each system. Then find
the solution from the graph.
8
x + 3y = -6
2x - 3y = -3
x + 3y = -6
-x
-x
3y = -x – 6
2x - 3y = -3
-2x
-2x
-3y = -2x – 3
6
4
2
-8 -6
-4
-2
-2
-4
y = -1/3 x - 2 y = 2/3 x + 1
(-3,-1)-6
-8
2
4
6
8
Example 5
Graph and classify each system. Then find
the solution from the graph.
8
x–y=2
x=4
x–y=2
-x
-x
-y = -x + 2
6
(4,2)
-8 -6
-4
4
2
-2
-2
-4
y=x–2
-6
-8
2
4
6
8
Example 6
Graph and classify each system. Then find
the solution from the graph.
9x  3y  3

21x  4  7y
 y  3x  1


4
 y  3x  7
There are no
solutions.
Notice that the slopes are the
same, but they don’t start at the
same point. They are parallel. What
does that tell us about this
problem?
You try it!
Solve the following systems of equations using
graphing.
1) y = ½x – 2
y = -2x + 3
4) x – y = -4
2x + y = 1
2) y = 2/3 x
3) y = -½x
y=x-1
y = -2x + 6
5) x + y = 4
6) 2x + 3y = 0
x + 2y = 2
y=2
Answers: 1) (2,-1)
2) (3,2)
3) (4,-2)
4) (-1,3) 5) (6, -2) 6) (-3,2)
More Practice
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