aa section 5-3
TRANSCRIPT
Section 5-3Solving Systems by Substitution
Warm-up1. Solve 8x + 8(5-2x) = -40
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 8(5-2x) = -40
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
-8x = -80
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
-8x = -80
x = 10
2. Evaluate 3x - 2 when x = 4y + 1
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
-8x = -80
x = 10
2. Evaluate 3x - 2 when x = 4y + 1
3(4y + 1) - 2
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
-8x = -80
x = 10
2. Evaluate 3x - 2 when x = 4y + 1
3(4y + 1) - 2
12y + 3 - 2
Warm-up1. Solve 8x + 8(5-2x) = -40
8x + 40 -16x = -40
8x + 8(5-2x) = -40
-8x + 40 = -40
-8x = -80
x = 10
2. Evaluate 3x - 2 when x = 4y + 1
3(4y + 1) - 2
12y + 3 - 2
12y + 1
1. Tables
1. Tables Not very efficient
1. Tables Not very efficient
2. Graphing by hand
1. Tables Not very efficient
2. Graphing by hand Not very accurate
1. Tables Not very efficient
2. Graphing by hand Not very accurate
3. Graphing Calculator
1. Tables Not very efficient
2. Graphing by hand Not very accurate
3. Graphing Calculator Cheap way out
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
x + y = 6
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
x + y = 6
2 + 4 = 6
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
x + y = 6
2 + 4 = 6
(2, 4)
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
x + y = 6
2 + 4 = 6
(2, 4)
Always check your answer.
Example 1Solve.
x + y = 6
y = x + 2
⎧⎨⎩⎪
x + (x + 2) = 6
2x + 2 = 6
2x = 4
x = 2
y = x + 2
y = 2 + 2
y = 4
x + y = 6
2 + 4 = 6
(2, 4)
Always check your answer.
You’ll know you’re right.
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
7/2 A = 1750
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
7/2 A = 1750
A = 500
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
7/2 A = 1750
A = 500
S = 1000
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
7/2 A = 1750
A = 500
S = 1000
C = 250
Example 2The Drama Club printed 1750 tickets for their spring play. They
printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and
find the number of each ticket printed.
A = adult tickets S = student tickets C = children tickets
⎧
⎨⎪
⎩⎪
A + S + C = 1750
S = 2A
C = 1/2 A
A + 2A + 1/2 A = 1750
7/2 A = 1750
A = 500
S = 1000
C = 250
They printed 500 adult tickets, 1000 student tickets, and 250 children’s tickets
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3 x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = 4(-3)
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = -12
y = 4(-3)
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = -12
y = 4(-3)
Check:
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = -12
y = 4(-3)
Check:
(3)(12) = 36
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = -12
y = 4(-3)
Check:
(3)(12) = 36
(-3)(-12) = 36
x2 = ± 9
Example 3Solve.
y = 4x
xy = 36
⎧⎨⎩⎪
x(4x) = 36
4x2 = 36
x2 = 9
x = 3 or x = -3
y = 4(3)
y = 12
y = -12
y = 4(-3)
Check:
(3)(12) = 36
(-3)(-12) = 36
(3, 12) or (-3, -12)
x2 = ± 9
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 74 = 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 74 ≠ 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Wait, what?
4 ≠ 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Wait, what?
3x + y = 7
4 ≠ 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Wait, what?
3x + y = 7
y = -3x + 7
4 ≠ 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Wait, what?
3x + y = 7
y = -3x + 7
Oh, parallel lines!
4 ≠ 7
Example 4Solve.
y = 4 − 3x
3x + y = 7
⎧⎨⎩⎪
3x + (4 - 3x) = 7
Wait, what?
3x + y = 7
y = -3x + 7
Oh, parallel lines!
4 ≠ 7
(No solutions)
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
3(2x2 ) = 6x2
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
3(2x2 ) = 6x2
6x2 = 6x2
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
3(2x2 ) = 6x2
6x2 = 6x2
This is always true!
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
3(2x2 ) = 6x2
6x2 = 6x2
This is always true!
These are the same graphs.
Example 5
y = 2x2
3y = 6x2
⎧⎨⎪
⎩⎪
Solve.
3(2x2 ) = 6x2
6x2 = 6x2
This is always true!
These are the same graphs.
Infinitely many solutions on the parabola
Consistent:
Consistent: A system with one or more solutions
Consistent: A system with one or more solutions
Inconsistent:
Consistent: A system with one or more solutions
Inconsistent: A systems with no solutions
Homework
Homework
p. 289 #1-20, skip 17, 18
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