Section 5-2
Solving Systems Using Tables or Graphs
Warm-up
Graph the following equations on the same graph.
a. y = 2/3x - 5
b. y = -x + 3
Warm-up
Graph the following equations on the same graph.
a. y = 2/3x - 5
b. y = -x + 3x
y
y = 2/3x - 5
y = -x + 3
How can we solve a system?
System:
System: Two sentences connected by “and”
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
Notation:
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
Notation:
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
Notation:
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
Solution Set of a System:
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
Notation:
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
Solution Set of a System: Since we’re using “and,” we are looking for what is in both sets/equations
System: Two sentences connected by “and”
y = 4x + 8 and y = 3x + 5
Notation:
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
Solution Set of a System: Since we’re using “and,” we are looking for what is in both sets/equations
**Often, it is just a point**
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
0
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
0 8 5
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
0 8 5 3
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01
8 5 3
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01
8 512 8
3
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01
8 512 8
34
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2
8 512 8
34
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2
8 512 80 -1
34
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2
8 512 80 -1
341
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2-3
8 512 80 -1
341
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2-3
8 512 80 -1-4 -4
341
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2-3
8 512 80 -1-4 -4
3410
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2-3
8 512 80 -1-4 -4
3410
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
a. Tables x y = 4x + 8 y = 3x + 5
01-2-3
8 512 80 -1-4 -4
3410
(x, y) = (-3, 4)
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc3. Choose 5: intersect
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc3. Choose 5: intersect
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc3. Choose 5: intersect
4. Choose the two equations
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc3. Choose 5: intersect
4. Choose the two equationsx
y
Example 1
Solve the system
y = 4x + 8
y = 3x + 5
⎧⎨⎩⎪
b. Graphing (by hand)
c. Graphing Calculator
1. Graph both equations
x
y
2. Press 2nd --> Calc3. Choose 5: intersect
4. Choose the two equationsx
y
(x, y) = (-3, 4)
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
w
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
l + 2w = 70
lw = 400
⎧⎨⎩⎪
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
l + 2w = 70
lw = 400
⎧⎨⎩⎪
Can we accurately solve this by graphing?
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
l + 2w = 70
lw = 400
⎧⎨⎩⎪
Can we accurately solve this by graphing?
(l, w) ≈ (14.4, 27.8)
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
l + 2w = 70
lw = 400
⎧⎨⎩⎪
Can we accurately solve this by graphing?
(l, w) ≈ (14.4, 27.8)(l, w) ≈ (55.6, 7.2)
Example 2
Matt Mitarnowski wants to enclose a 400-square meter rectangular garden with 70 meters of fencing. To do
this, Matt must use one side of his barn as a side of the garden. What can the dimensions of the garden be?
Barn l
w
ww = width, l = length
l + 2w = 70
lw = 400
⎧⎨⎩⎪
Can we accurately solve this by graphing?
(l, w) ≈ (14.4, 27.8)(l, w) ≈ (55.6, 7.2)
14.4m x 27.8m or55.6m x 7.2 m
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
a. Table
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
0
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
0 0 1
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
0 0 1 1
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01
0 1 1
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01
0 15 -2
1
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01
0 15 -2
17
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1
0 15 -2
17
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1
0 15 -2-5 4
17
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1
0 15 -2-5 4
17-9
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1
0 15 -2-5 4
17-9
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1
0 15 -2-5 4.5 .7
17-9
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1
0 15 -2-5 4.5 .7
17-9.2
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1.2
0 15 -2-5 4.5 .7
17-9.2
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1.2
0 15 -2-5 4.5 .71 .4
17-9.2
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1.2
0 15 -2-5 4.5 .71 .4
17-9.2.6
Example 3
Solve
y = 5x
y = −3x +1
⎧⎨⎩⎪
x y = 5x y = -3x + 1a. Table
01-1.1.2
0 15 -2-5 4.5 .71 .4
17-9.2.6
How long do we try this?
Example 3
Solve
b. Graphing (by hand)
y = 5x
y = −3x +1
⎧⎨⎩⎪
Example 3
Solve
b. Graphing (by hand)
y = 5x
y = −3x +1
⎧⎨⎩⎪
c. Graphing Calculator
Example 3
Solve
b. Graphing (by hand)
y = 5x
y = −3x +1
⎧⎨⎩⎪
c. Graphing Calculatorx
y
Example 3
Solve
b. Graphing (by hand)
y = 5x
y = −3x +1
⎧⎨⎩⎪
c. Graphing Calculatorx
y
x
y
Example 3
Solve
b. Graphing (by hand)
y = 5x
y = −3x +1
⎧⎨⎩⎪
c. Graphing Calculatorx
y
x
y(x, y) = (.125, .625)
Homework
Homework
p. 282 #1-24
“Lack of money is no obstacle. Lack of an idea is an obstacle.” - Ken Hakuta
Top Related