3.4 Applications of Systems of Equations
Presentation
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Mathematics
•
9th Grade
•
Medium
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Standards-aligned
Rayne Young
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7 Slides • 11 Questions
1
By Rayne Young
2
Multiple Choice
A ______ is a set of two or more equations that have the same variables.
3
Multiple Choice
The ordered pair that satisfies all equations in the system is the
4
Multiple Choice
When solving a system of equations algebraically, which statement results in infinite solutions?
4 = 7
2 = 2
-3 = 3
all of the above
5
Multiple Choice
When solving a system of equations, which statement results in no solution?
4 = 7
-2 = 2
0 = 3
all of the above
6
Given two equations & the method, can you determine proper steps in solving?
7
Elimination
Given x = 2y + 1 and 2x + 3y = 12.
1) Plug in for x
2(2y + 1) + 3y = 12
2) Simplify
4y + 2 + 3y = 12
7y + 2 = 12
3) Solve for y
4) Plug back in & solve for x
Substitution
Given -3x + 4y = 24 and 2x + 3y = 12.
1) SAME coefficient w/ OPPOSITE signs (multiply x or y by opposite coefficient)
2(-3x + 4y = 24)
3 (2x + 3y = 12)
2) Add down
0x + 17y = 84
3) Solve for y
4) Plug back in & solve for x
-6x+8y=48
6x+9y=24
8
Multiple Select
A system of equations is shown below.
4x−5y=−10
2x−7y =4
Which operations on the system of equations will isolate the y quantity?
(There are two correct options.)
Cancel the y's by multiplying the top by 2 & bottom by 4.
Cancel the x's by multiplying the top by 2 & bottom by 4 (make one negative).
Cancel the x's by multiplying the top by 4 & bottom by 2.
Cancel the y's by multiplying the top by 7 & bottom by 5 (make one negative).
Cancel the y's by multiplying the top by 5 & bottom by 7.
9
Multiple Choice
The substitution method will be used to solve this system of equations.
x=7−2y
2x−7y =3
Which equation would lead to a correct solution with this method?
(7−2y)+2y=7
(7+2y)+2y=7
2(7−2y)−7y=3
2(7+2y)−7y=3
10
Given a word problem, can you write the 2 equations to model the situation?
11
Don't forget to define your variables!
Then, use the info from the word problem to pair variables with the numbers that go with them.
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes and 14 large boxes for a total of $203. Ming sold 11 small boxes and 11 large boxes for a total of $220. Find the cost each of one small box and one large box of oranges.
x = cost of small boxes
y = cost of large boxes
Matt: 3x + 14y = 203
Ming: 11x + 11y = 220
12
Multiple Choice
y = 8.40 + x
y = 8.40x + 58
y = 8.40x
y = 8.40x - 58
13
Multiple Choice
On Monday Mr. Beignet bought 10 coffees and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of each item?
10c + 5d = 14.25
5c + 10d = 16.50
10c + 5d = 16.50
5c + 10d = 14.25
c + d = 10
5c + 10d = 16.50
c + d = 5
5c + 10d = 16.50
14
Multiple Choice
2p + 3b = 23
2p + 3b = 29.50
2b + 3p = 23
5bp = 23
15
Given the solution in context, can you explain what each number represents?
16
Give context to your answers!
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes and 14 large boxes for a total of $203. Ming sold 11 small boxes and 11 large boxes for a total of $220. Find the cost each of one small box and one large box of oranges.
x = cost of small boxes
y = cost of large boxes
Matt: 3x + 14y = 203
Ming: 11x + 11y = 220
Small boxes (x) cost $7.
Large boxes (y) cost $13.
After solving, you find get (7,13), or x=7 & y=13 . What do these numbers mean?
17
Multiple Choice
Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. After solving the system below, Alexandra gets a solution of (45,90)
3x + 2y = 315
2x + 4y = 450
What does the solution (45,90) mean?
Hair dyes take Alexandra 45 minutes & haircuts take 90 minutes.
Haircuts take Alexandra 45 minutes & hair dyes take 90 minutes.
Haircuts cost $45 & hair dyes cost $90.
Hair dyes cost $45 & haircuts cost $90.
18
Multiple Choice
Caroline is considers 2 video game rental plans. Plan A can be modeled with the equation C=2n , and Plan B is modeled with the equation C=n+6 , where C represents the cost in dollars & n represents the number of games rented each month. The solution to this situation is n=6 & C=12 . What do these numbers mean?
Caroline can order 12 games from Plan A & 6 games from Plan B.
If Caroline orders 12 games each month, both plans will cost $6.
Caroline can order 6 games from Plan A & 12 games from Plan B.
If Caroline orders 6 games each month, both plans will cost $12.
By Rayne Young
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