6.1 Solving Linear Systems by
Graphing
Standard: SWBAT solve a system of
two linear equations in two variables
and are able to interpret the answer
graphically.
http://apod.nasa.gov/apod/ap081212.html
Lick Observatory Moonrise
Mini Quiz 48
Is the ordered pair a solution to the equation
2x – 3y = 5
1. (1, 0)
2. (4, 1)
3. Graph the line 2x – y + 3 = 0
Overview



Solving Systems of Linear Equations (two
equations) by Graphing
Understanding No Solution
Understanding Infinite Solution
Graphing Lines Quick Review
What are the different ways to graph a line?
 T-chart
 Slope-Intercept Form: y = mx + b
 x- and y-intercepts: Using Standard Form:
Ax + By = C
Graph the line x – 2y – 4 = 0
Graphing Systems of Linear Equations
Step:
1. Graph each line on the same coordinate
plane
2. Label the point (ordered pair) where the
lines cross (intersect)
3. Check your answer (YES, you need to
check both equations!)
Graphing Lines
Solve the Systems by Graphing
1. y  3x  1
y  2 x  4
Check: (1, 2)
y = 3x – 1
2 = 3(1) – 1
2=3–1
2=2 
y = -2x + 4
2 = -2(1) + 4
2 = -2 + 4 Where do the lines cross?
2=2
(1, 2)
Graphing Lines
Solve the Systems by Graphing
2. y  4 x  7
y  3x
Check: (1, -3)
y = -3x
y = 4x – 7
-3 = 4(1) – 7 -3 = -3(1)
-3 = -3 
-3 = 4 – 7
-3 = -3 
Where do the lines cross?
(1, -3)
Graphing Lines
Solve the Systems by Graphing
3. y  2 x  7
y  x6
Check: (-1, 5)
y=x+6
y = 2x + 7
Where do the lines cross?
5
=
(-1)
+
6
5 = 2(-1) + 7
(-1, 5)
5=5
5 = -2 + 7
5=5
Special Cases – No Solution and
Infinitely Many Solutions
No Solutions
Infinitely Many Solutions
y  x  4
4. y  2 x  6 y  2 x  6 6. x  y  4
4x  2 y  8 y  2x  4
2x  2 y  8 y  x  4
Same slope
Same slope
Different y-intercept
Same y-intercept
1
y   x5
3
x

2
y

10
2
5.
7. 3x  5 y  0
y x
5
1
5
3
2 x  4 y  10 y   x 
3
y x
2
2
y x
5
5
Solve for y and look at the equations, what do you
notice about the equations?
Graphing Lines
Solve the Systems by Graphing
8. y   x  2
3x  3 y  12
x-intercept (x, 0)
3x = 12
x = 4 (4, 0)
y-intercept (0, y) Where do the lines cross?
3y = 12
No Solution
y = 4 (0, 4)
Graphing Lines
Solve the Systems by Graphing
9. y  3x  3
3x  y  3
x-intercept (x, 0)
3x = -3
x = -1 (-1, 0)
y-intercept (0, y)
y = -3 (0, -3)
Where do the lines cross?
Infinitely Many Solutions
Graphing Lines
Solve the Systems by Graphing
10. 2 x  y  0
y  2 x  4
Slope-intercept form
2x + y = 0
y = -2x
Where do the lines cross?
No Solution
Application
35
11. Suppose you have $20 in
y = 5x + 20
y = 10x + 5
After 3 weeks!
Amount Saved
your bank account. You start
saving $5 each week. Your
friend has $15 in her account
and is saving $10 each week.
When will you and your friend
have the same amount of
money in your account?
30
25
20
15
10
5
1 2 3 4 5 6
Number of Weeks
Wrap Up

Solving Linear System by Graphing
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Graph each line
Find where they cross
Check solution
HW: P. 279 #13-23 odd, P. 281 #43-51 odd
DLUQ: When graphing a linear system, where do
you find the solution?