Algebra
7.1 Solving Linear Systems by Graphing
System of Linear Equations
(linear systems)
 Two equations with two variables.
An example:
4x + 5y = 3
2x = 6y -10
 A solution to a linear system is an ordered
pair (x, y) that, when substituted in, makes
both equations true.
 Thus, the solution would be on both graphs.
The solution(s) is the intersection of the lines.
Is the ordered pair a solution to the
system of equations? Yes or no.
 -2x + y = -11
(6, 1)
-x – 9y = 15
Plug it in and check!
-2(6) + (1) = -11?
-12 + 1 = -11?
-11 = -11 Yes.
-(6) – 9(1) = 15?
-6 – 9 = 15?
-15 = 15? No.
The point is not a solution to the system of equations.
Use the graph to find the solution to the system of
equations. Then check your solution algebraically.
 y = 3x -12
y = -2x + 3
The solution seems to
be (3, -3). Check this
solution algebraically on your
paper. Who can
check it on the board?
Yes. The point is a solution
to the system.
Steps to “Graphing to Solve a Linear System”
1)
Write each equation in a form that is easy to graph (Slope-int
or standard)
2)
Graph both equations on the same coordinate plane
3)
Find the point of intersection
4)
Check the point algebraically in the system of equations
Solve the system graphically. Check
the solution algebraically.

3x – 4y = 12
-x + 5y = -26
Step 1) Put the equations in a graph-able
form.
3x – 4y = 12 Find the x-int. and y-int.
3(0) – 4y = 12
-4y = 12
y = -3 The y-int is (0, -3) Graph it!
3x – 4(0) = 12
3x = 12
x = 4 The x-int is (4, 0) Graph it!
Put -x + 5y = -26 into slope-int form.
+x
+x
5y = x – 26
y = 1/5 x – 5 1/5
The solution to the system
seems to be (-4, -6)
.
.
.
.
Check (-4, -6) in the system algebraically.
 3x - 4y = 12
(-4, -6)
-x + 5y = -26
3(-4) - 4(-6) = 12?
-12 + 24 = 12?
12 = 12 Yes.
-(-4) + 5(-6) = -26?
4 – 30 = -26?
-26 = -26 Yes.
The point is a solution to the system of equations.
You try! Solve the system graphically.
Check the solution algebraically.

3x + y = 11
x - 2y = 6
Step 1) Put the equations in a graphable form.
3x + y = 11 Put into slope-int form.
-3x
-3x
y = -3x + 11 Graph it!
x - 2y = 6 Put into slope-int form.
-x
-x
-2y = -x + 6
y = 1/2 x – 3 Graph it!
The solution to the system
seems to be (4, -1)
.
.
.
.
.
Check (4, -1) in the system algebraically.
 6x + 2y = 22
(4, -1)
x - 2y = 6
6(4) + 2(-1) = 22?
24 - 2 = 22?
22 = 22 Yes.
(4) - 2(-1) = 6?
4 + 2 = 6?
6 = 6 Yes.
The point is a solution to the system of equations.
HW
 P. 401-403 #11-19 Odd, 25-33 Odd, 47-59
Odd