Download 2 Graphing

5 minutes
Warm-Up
1) On the coordinate plane, graph two lines
that will never intersect.
2) On the coordinate plane, graph two lines
that intersect at one point.
3) On the coordinate plane, graph two lines
that intersect at every point (an infinite
number of points).
Solving Systems of Equations
by Graphing
Objectives:
•To find the solution of a system of equations by
graphing
Activity
With your partner:
Partner 1 - graph the equation 2x + 3y = 12
Partner 2 - assist partner 1
Partner 2 - graph the equation x – 4y = -5
Partner 1 - assist partner 2
How many points of intersection are there? 1
Activity
With your partner:
Partner 1 - graph the equation x = 2y + 1
Partner 2 - assist partner 1
Partner 2 - graph the equation 3x – 6y = 9
Partner 1 - assist partner 2
How many points of intersection are there? 0
Activity
With your partner:
Partner 1 - graph the equation 2x = 4 - y
Partner 2 - assist partner 1
Partner 2 - graph the equation 6x + 3y = 12
Partner 1 - assist partner 2
How many points of intersection are there?
an infinite number
Example 1
Solve the following system by graphing.
x+y=2
x+y=2
x=y
x
y
0
1
5
8
6
4
2
-8 -6
-4
-2
-2
-4
-6
-8
(1,1)
2
4
2
1
-3
x=y
6
8
x
y
0
1
5
0
1
5
Practice
Solve by graphing.
1) x + 4y = -6
2x – 3y = -1
2) y + 2x = 5
2y – 5x = 10
4 minutes
Warm-Up
Solve by graphing.
1) y – 2x = 7
y = 2x + 8
2) 3y – 2x = 6
4x – 6y = -12
Solving Systems of Equations
by Graphing pt. 2 Check a
Solution:
Objectives:
•To determine whether an ordered pair is a solution
of a system of equations
Example 1
Determine whether (3,5) is a solution of the
system.
 y  4x  7

x  y  8
y = 4x - 7
x+y=8
5 = 4(3) - 7
5 = 12 - 7
5=5
3 + 5= 8
8=8
(3,5) is a solution of the system
Example 2
Determine whether (-2,1) is a solution of
the system.
2x  y  5

3x  2y  3
2x – y = -5
3x + 2y = 3
2(-2) - 1 = -5
-4 – 1 = -5
-5 = -5
3(-2) + 2( 1 ) = 3
-6 + 2 = 3
(-2,1) is not a solution of the system
Practice
Determine whether the given ordered pair is
a solution of the system.
1) (2,-3); x = 2y + 8
2x + y = 1
2) (-3,4); 2x = -y – 2
y = -4
Practice
Solve these systems by graphing.
1) x + 4y = -6
2x – 3y = -1
2) y + 2x = 5
2y – 5x = 10