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Unit 10: Systems of Linear Equations/Inequalities
Solve Linear Systems by Multiplying First
1. What is the least common multiple of 12 and 18?
36
2x – 3y = -4
2. Explain how to solve the linear system using the
elimination method.
7x + 9y = -5
Multiply equation 1 by 3 and add to Equation 2.
Then solve for x and substitute to find y.
Solve the linear system using elimination.
3. 4x – 3y = 8
4. -2x – 5y = 9
5. 7x – 6y = -1
5x – 2y = -11
3x + 11y = 4
5x – 4y = 1
(-7, -12)
(-17, 5)
(5, 6)
6. 3x + 2y = 4
7. 4x – 5y = 18
8. 8x – 9y = -15
2y = 8 – 5x
3x = y + 11
-4x = 19 + y
4 10
5
1
(2, -1)
(3 , - )
(-4
, -2 )
11 11
22
11
9. 0.3x + 0.1y = -0.1
10. 4.4x – 3.6y = 7.6
11. 3x – 2y = -20
-x + y = 3
x–y=1
x + 1.2y = 6.4
(-1, 2)
(5, 4)
(-2, 7)
12. 0.2x – 1.5y = -1
13. 1.5x – 3.5y = -5
14. 4.9x + 2.4y = 7.4
x – 4.5y = 1
-1.2x + 2.5y = 1
0.7x + 3.6y = -2.2
(10, 2)
(20, 10)
(2, -1)
15. A rectangle has a perimeter of 18 inches. A new
rectangle is formed by doubling the width w and
tripling the length ℓ, as shown. The new rectangle
P = 46 in.
has a perimeter P of 46 inches.
a. Write and solve a system of linear equations to
find the length and width of the original
3ℓ
rectangle.
2ℓ + 2x = 18
3(2ℓ) + 2(2w) = 46; 6ℓ + 4w = 46
b. Find the length and width of the new rectangle.
Length = 15 inches; Width = 8 inches
2w
16. The table shows the number of apples needed to make the apple pies and applesauce sold at a
farm store. During a recent apply picking at the farm store. During a recent apple picking at
the farm, 169 Granny Smith apples and 95 Golden Delicious apples were picked. How many
apple pies and batches of applesauce can be made if every apple is used?
Type of apple
Needed for a pie
Needed for a batch of applesauce
Granny Smith
5
4
Golden Delicious
3
2
p = pies
a = applesauce
5p + 4a = 169
3p + 2a = 95
Pies = 21; Batches of Applesauce = 16
17. Tickets for admission to a high school football game cost $3 for students and $5 for adults.
During one game, $2995 was collected from the sale from 729 tickets.
a. Write and solve a system of linear equations to find the number of tickets sold to
students and the number of tickets sold to adults.
s = student tickets
a = adult tickets
3s + 5a = 2995
s + a = 729
325 student tickets and 404 adult tickets
b. Graph the system of linear equations. Use the graph to determine whether your answer
to part (a) is reasonable.
18. A dim sum restaurant offers two sizes of dishes;
small and large. All small dishes cost the same
and all large dishes cost the same. The bills show
the cost of the food before the tip is included.
What will 3 small and 2 large dishes cost before
the tip is included? Explain.
s = small
L = large
3s + 5L = 28.20
4s + 3L = 23.30
Small dish = $2.90 and a large dish = $3.90
3(2.90) + 2(3.90) = 16.50
3 small
5 large
$28.20
4 small
3 large
$23.30