int math 2 section 8-4 1011
DESCRIPTION
Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)TRANSCRIPT
Section 8-4Solve Systems by Adding, Subtracting, and
Multiplying (Linear Combinations)
Sun, Apr 10
Essential QuestionsHow do you solve systems of equations by adding and subtracting?
How do you solve systems of equations by adding and multiplying?
Where you’ll see this:
Landscaping, construction, sports
Sun, Apr 10
Why another method?
Sun, Apr 10
Why another method?
Graphing: Problems with accuracy
Sun, Apr 10
Why another method?
Graphing: Problems with accuracy
Substitution: Need an isolated variable
Sun, Apr 10
Why another method?
Graphing: Problems with accuracy
Substitution: Need an isolated variable
Combinations: Could speed up process
Sun, Apr 10
Why another method?
Graphing: Problems with accuracy
Substitution: Need an isolated variable
Combinations: Could speed up process
Look at the system to determine best method
Sun, Apr 10
Solve by Combinations
Sun, Apr 10
Solve by Combinations1. Choose a variable to eliminate (your choice).
Sun, Apr 10
Solve by Combinations1. Choose a variable to eliminate (your choice).
2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations.
Sun, Apr 10
Solve by Combinations1. Choose a variable to eliminate (your choice).
2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations.
3. Solve for the remaining variable.
Sun, Apr 10
Solve by Combinations1. Choose a variable to eliminate (your choice).
2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations.
3. Solve for the remaining variable.
4. Plug back into an original equation to find the other variable.
Sun, Apr 10
Solve by Combinations1. Choose a variable to eliminate (your choice).
2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations.
3. Solve for the remaining variable.
4. Plug back into an original equation to find the other variable.
5. Check and rewrite the answer.
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
−2x + 3 y = 2
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
−2x + 3 y = 2
2x + 7 y = 18
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
−2x + 3 y = 2
2x + 7 y = 18
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
10 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 210 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
10 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2
10 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
10 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
−2(2)+ 3(2) = 2
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
−2(2)+ 3(2) = 2 −4 + 6 = 2
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
−2(2)+ 3(2) = 2 −4 + 6 = 2
2(2)+ 7(2) = 18
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
−2(2)+ 3(2) = 2 −4 + 6 = 2
2(2)+ 7(2) = 18 4 + 14 = 18
Solve by combining the equations
Sun, Apr 10
Example 1
a.
−2x + 3 y = 22x + 7 y = 18
⎧⎨⎪
⎩⎪
10 y = 20
−2x + 3 y = 2
2x + 7 y = 18
y = 2
−2x + 3(2) = 2
−2x + 6 = 2 −6 −6
−2x = −410 10 −2 −2 x = 2
Check:
−2(2)+ 3(2) = 2 −4 + 6 = 2
2(2)+ 7(2) = 18 4 + 14 = 18
(2, 2)
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1)
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 9
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 4
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
10(1)+ 4(1) = 14
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
10(1)+ 4(1) = 14
10 + 4 = 14
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
10(1)+ 4(1) = 14
10 + 4 = 14
1+ 4(1) = 5
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
10(1)+ 4(1) = 14
10 + 4 = 14
1+ 4(1) = 5 1+ 4 = 5
Solve by combining the equations
Sun, Apr 10
Example 1
b.
10x + 4 y = 14x + 4 y = 5
⎧⎨⎪
⎩⎪( ) (−1) 10x + 4 y = 14 −x − 4 y = −5
9x = 99 9
x = 1
1+ 4 y = 5 −1 −1
4 y = 44 4
y = 1
Check:
10(1)+ 4(1) = 14
10 + 4 = 14
1+ 4(1) = 5 1+ 4 = 5
(1,1)
Solve by combining the equations
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −17
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16 +2 +2
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
7(−1)+ 2(6) = 5
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
7(−1)+ 2(6) = 5 −7 + 12 = 5
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
7(−1)+ 2(6) = 5 −7 + 12 = 5
2(−1)+ 3(6) = 16
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
7(−1)+ 2(6) = 5 −7 + 12 = 5
2(−1)+ 3(6) = 16
−2 + 18 = 16
Sun, Apr 10
Example 2Solve by combining the equations
7x + 2 y = 52x + 3 y = 16
⎧⎨⎪
⎩⎪
( ) (3)( ) (−2)
21x + 6 y = 15 −4x − 6 y = −32
17x = −1717 17
x = −1
2(−1)+ 3 y = 16
−2 + 3 y = 16
3 y = 18 +2 +2
3 3
y = 6
Check:
7(−1)+ 2(6) = 5 −7 + 12 = 5
2(−1)+ 3(6) = 16
−2 + 18 = 16
(−1,6)
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −43
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
5(10)+ 2(− 432) = 7
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
5(10)+ 2(− 432) = 7
50 − 43 = 7
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
5(10)+ 2(− 432) = 7
50 − 43 = 7
4(10)+ 2(− 432) = −3
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
5(10)+ 2(− 432) = 7
50 − 43 = 7
4(10)+ 2(− 432) = −3
40 − 43 = −3
Sun, Apr 10
Example 3Solve by combining the equations
5x + 2 y = 74x + 2 y = −3
⎧⎨⎪
⎩⎪( ) (−1)
5x + 2 y = 7
−4x − 2 y = 3
x = 10
5(10)+ 2 y = 7
50 + 2 y = 7 −50 −50
2 y = −432 2
y =
−432
Check:
5(10)+ 2(− 432) = 7
50 − 43 = 7
4(10)+ 2(− 432) = −3
40 − 43 = −3
(10,− 432)
Sun, Apr 10
Problem Set
Sun, Apr 10
Problem Set
p. 350 #1-27 odd
“A verbal contract isn’t worth the paper it’s written on.” - Samuel Goldwyn
Sun, Apr 10