# System of Linear Equations

```Warm ups

What is the slope and y intercept?
1
y   x3
2
2x  3 y  6
y  1  2( x  5)
8.1 Graphing Systems of
Equations
Objective: To solve systems of
equations by graphing.
System of Linear Equations:
System of Linear Equations: Two
or more linear equations.
 A solution to the system of linear
equations is any ordered pair that
makes BOTH equations true.
Three Types of Solutions:
 Intersection is Solution
One Solution
Different slope
Different y-intercept
“Intersect at one point”
No Solution
Same slope
Different y-intercept
“Run parallel  Never intersect”
Infinite Solutions
Same slope
Same y-intercept
“Same line  Intersect infinitely”
Examples: Solve each system by graphing.
1) y = –x + 1
y = 2x + 4
y = –x + 1
y = 2x + 4
Slope: -1
Slope: 2
Y-int: (0, 1)
Y-int: (0, 4)
Different slope
Different y-intercept
“Intersect at one point”
The solution of the system is: (-1, 2)
x = –1, y = 2
2) x + y = 1
y = –x + 3
x+y=1
–x
–x
y=-x+1
y = –x + 3
Slope: -1
Y-int: (0, 3)
Slope: –1
Y-int: (0, 1)
Same slope
Different y-intercept
“Run parallel  Never intersect”
The solution of the system is: no solution
3) x – 2y = 4
2x – 4y = 8
x – 2y = 4
–x
–x
–2y = –x + 4
–2
–2 –2
y =&frac12;x–2
2x – 4y = 8
–2x
–2x
–4y = –2x + 8
–4
–4 –4
Y=&frac12;x–2
Slope: &frac12;
Slope: &frac12;
Y-int: (0, –2)
Y-int: (0, –2)
Same slope
Same y-intercept
“Same line  Intersect infinitely”
The solution of the system is: infinite solutions
Try with a Partner:
4) y = 3x – 3
x+y=1
y = 3x – 3
Slope: 3
x+y=1
–x
–x
y = –x + 1
Y-int: (0, –3 ) Slope: –1
Y-int: (0, 1)
Different slope
Different y-intercept
“Intersect at one point”
The solution of the system is: (1, 0)
x = 1, y = 0
Summarize:
Number of
Solutions
1
(Ordered Pair)
Slope
Y-Intercept
Different
Same
Different
0
(No Solution)
∞
(Infinitely
Many)
Same
Different
Same
Same
TRY ON OWN
the four multiple choice
questions on the elmo.
Speaker and Scribe Review
1 1
3
x 
x
2 5
10
3x  2  x  4
3
x  33
8
x  3
x  88
Review
5x  1 1

8
2
2
2 x  48
5
x x5

8
6
3
x
5
x  20
x  20
Review
5 x  10
5
6
x4
10  3x  6 x  8
x6
6 x  2  5( x  3)  x
NOsolution
Write in STANDARD
(1, 2)(1,8)
5x  y  3
1
( 4, 6) m 
2
x  2y  8
Determine Value of r.
5
(4, r )( r , 2) m 
r7
3
3
(3, r )(r ,5)m 
5
r 8
Homework
8.1 Graphing Systems of
Linear Equations
(2 sides)
```