Download 11_03 - Solving Systems of Equations by Graphing

1) Graph y = 2x + 1
using slope & intercept
2) Graph x + 2y = 2
using x & y intercepts
2
The slope is 2 
1
x intercept = 2
(2,0)
y intercept is ( 0 , 1 )
y intercept = 1
(0,1)
11.03
Solving a System
of Equations by
Graphing
Remember, a solution to a system of
equations is an ordered pair ( x , y ) that
make both equations true.
One method for finding a solution to a
system is using the graphing method.
To solve a system of equations by graphing,
graph each equation on the same coordinate
plane and find the coordinates ( x , y ) of the
point where the two lines meet.
These coordinates ( x , y ) are the x and y
values that are the solution to the system.
Find the solution to the following system.
y = – 3x + 2
y = 2x – 3
Graph: y = – 3x + 2
Graph: y = 2x – 3
Find the point where
the 2 lines meet
Find the coordinates
of that point.
(1,–1)
( 1 , – 1 ) is the solution to the system.
Find the solution to the following system.
x + y = 1
y = 2x + 4
Graph: x + y = 1
Graph: y = 2x + 4
Find the point where
the 2 lines meet
Find the coordinates
of that point.
(–1,2)
( – 1 , 2 ) is the solution to the system.
Some systems do not have a solution.
y = 3x – 2
y = 3x + 3
Graph: y = 3x – 2
Graph: y = 3x + 3
Find the point where
the 2 lines meet
The lines do not meet.
They are parallel.
What does this mean ?
There is no solution to the system.
Some systems have infinite solutions.
2x + 2y = 4
y = –x + 2
Graph: 2x + 2y = 4
Graph: y = – x + 2
Find the point where
the 2 lines meet
What two lines?
They’re the same line.
What does this mean ?
There are infinite solutions, whatever numbers ( x , y )
work in the 1st equation will work in the 2nd.
Try This:
Find the solution to the following system.
x + y = 4
y = 2x – 5
Graph: x + y = 4
Graph: y = 2x – 5
Find the point where
the 2 lines meet
Find the coordinates
of that point.
(3,1)
( 3 , 1 ) is the solution to the system.