Download 3.1 Solving Linear Systems by Graphing

1.1 Solving Linear Systems by
Graphing
9/14/12
Vocabulary
System of 2
Linear Equations:
A system consisting of two linear
equations in two variables.
Ex: 6x – 2y = 8
3x – y = 4
Solution of a system
of 2 linear equations:
Is an ordered pair (x, y) that
satisfies both equations.
Graphically, it’s the point where
the lines intersect.
Example 1
Solve a System by Graphing
Solve the system by graphing. Then check your
solution algebraically.
Equation 1
3x – y = 3
ANSWER
Equation 2
x + 2y = 8
( 2, 3 )
Example 1
Solve a System by Graphing
You can check the solution by substituting 2 for x and 3
for y into the original equations.
Equation 1
Equation 2
3x – y = 3
x + 2y = 8
3( 2) – 3 =? 3
? 8
2 + 2( 3) =
? 3
6 – 3=
? 8
2 +6 =
3=3
8=8
ANSWER
The solution of the system is ( 2, 3 ).
Solve a System by Graphing
Checkpoint
Solve the system by graphing. Then check your solution.
1. y = – x + 3
y = 2x + 9
ANSWER
( –2, 5 )
Solve a System by Graphing
Checkpoint
Solve the system by graphing. Then check your solution.
2. x – 3y = 1
–x + y = – 1
ANSWER
( 1, 0 )
Solve a System by Graphing
Checkpoint
Solve the system by graphing. Then check your solution.
3. – x + 4y = 2
2x – 3y = 6
ANSWER
( 6, 2 )
Number of Solutions
1 solution
: the lines have
different slopes
Infinitely many
solutions
:the lines have the
same equation.
No solution
:the lines are parallel
(same slope)
Homework
1.1 #1, 3, 5, 7-14