Name ________________________________________ Date __________________ Class __________________
LESSON
11-2
Solving Linear Systems by Substitution
Practice and Problem Solving: C
Solve each system by substitution. Check your answer.
1. ⎧4 x − 9 y = 1
⎨
⎩ 2 x + y = −5
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2. ⎧ 1
⎪⎪ 2 x + y = 2
⎨
⎪ 2 x − 1 y = 28
⎪⎩ 3
4
3. ⎧2 x + 4 y = 1
⎨
⎩ x + 6y = 1
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Write a system of equations to solve.
4. Aaron is three times as old as his son. In ten years, Aaron will be twice
as old as his son. How old is Aaron now?
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5. Kitara has 100 quarters and dimes. Their total value is $19. How many
of each coin does Kitara have?
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6. A cleaning company charges a fixed amount for a house call and a
second amount for each room it cleans. The total cost to clean six
rooms is $250 and the total cost to clean eight rooms is $320.
How much would this company charge to clean two rooms?
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7. Willie Mays and Mickey Mantle hit 88 home runs one season to lead
their leagues. Mays hit 14 more home runs than Mantle that year.
How many home runs did Willie Mays hit?
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8. Coco has a jar containing pennies and nickels. There is $9.20 worth
of coins in the jar. If she could switch the number of pennies with the
number of nickels, there would be $26.80 worth of coins in the jar.
How many pennies and nickels are in the jar?
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9. Fabio paid $15.50 for five slices of pizza and two sodas. Liam paid
$19.50 for six slices of pizza and three sodas. How much does a slice
of pizza cost?
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6. 2, −6; 2, −6; infinite number of solutions
10. 27 years old
11. length = 37.5 inches and width =
12.5 inches
12. 25 hours at the weekday job and 15 hours
at the weekend job
13. Graphs will vary. The solution found by
graphing should agree with the solution by
substitution.
Practice and Problem Solving: C
1. (−2, −1)
7. −4, 2; 6, −3; no solution
2. (36, −16)
⎛1
3. ⎜ ,
⎝4
1⎞
8 ⎟⎠
4. 30 years old
5. 60 quarters and 40 dimes
6. $110
7. 51
8. 520 pennies and 80 nickels
Reading Strategies
9. $2.50
1. Possible answer 4x + y = 6,
−2x + y = 3
Practice and Problem Solving:
Modified
2. Disagree. Two lines can intersect at only
one point, are the same line and intersect
at an infinite number of points, or are
parallel and don’t intersect.
2. y
3. y
5. 5y + 5
3. one
6. 6y − 16
4. Both equations have slope of 3 and
different y-intercepts so the lines are
parallel and don’t intersect.
8. (5, 4)
9. (17, −24)
10. (5, 1)
5. infinite number of solutions
11. (4, −7)
Success for English Learners
12. (−1, −2)
1. The ordered pair makes both equations
true.
14. 9 dimes
15. $15
2. You find the point where the two lines
intersect.
Reading Strategies
LESSON 11-2
1. y = 5 − x or y = −x + 5
Practice and Problem Solving: A/B
2. The first equation is already solved for y.
1. (−1, −3)
2. (3, −1)
3. (2, 7)
4. (1, −4)
5. (5, −2)
6. (3, −2)
7. (1, −2)
8. (−1, −2)
3. The solution of a system must satisfy both
equations.
4. (6, 4)
5. (−3, 5)
9. (4, 9)
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