Equations and inequalities · Ages 13–14

Solving by substitution worksheet

Part of: Simultaneous linear equations

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Equations and inequalities · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.y = 2x, 5x + 2y = 54, x =
Answer:
2.y = 4x + 14 and 3x + y = −7: substituting, 3x + (4x + 14) = −7, so x = and y = .
Fill in each blank
Answer:
3.y = 4x, 4x + y = −24, x =
Answer:
4.x = y + 7, 2x − 5y = 26: x = , y =
Fill in each blank
Answer:
5.6x + 4y = 24, x − y = 9. The second gives x = y + 9; put it into the first: y =
Answer:
6.2x − 4y = −34, 4x − y = −5: x = , y =
Fill in each blank
Answer:
7.3x + 3y = −3, 4x + y = 2: x = , y =
Fill in each blank
Answer:
8.The simultaneous equations 2x + 3y = 23 and y = 3x + k have the solution x = 4. k =
Answer:

9.Putting y = 4x − 6 into 5x − 3y = −17, which line is right?
- A. 5x − 3(4x − 6) = −17
- B. 5x − 3(4x + 6) = −17
- C. 5x − 12x − 6 = −17
- D. 5(4x − 6) − 3y = −17
Choose the right answer
Answer:
10.The solution of y = 4x + 14 and 2x + 3y = 14 is x = −2, y = 6.
True or false?
Answer:
11.The solution of y = 4x − 17 and 2x + 4y = 4 is x = 4, y = 0.
True or false?
Answer:
12.Putting y = 3x − 1 into 8x − 5y = −16, which line is right?
- A. 8(3x − 1) − 5y = −16
- B. 8x − 15x − 1 = −16
- C. 8x − 5(3x − 1) = −16
- D. 8x − 5(3x + 1) = −16
Choose the right answer
Answer:

13.A father is 44 years older than his son and 5 times as old. With the father x and the son y: x = y + 44 and x = 5y, so 5y = y + 44, y = and x = .
Fill in each blank
Working:
Answer:
14.A purse holds only $10 and $5 coins, 20 in all, worth $155. How many $10 coins are there?
Working:
Answer:
15.Two numbers add to 114, and the larger is 6 more than 5 times the smaller. What is the larger number?
Working:
Answer:
16.A rectangle is 8 cm longer than it is wide, and its perimeter is 32 cm. How long is it, in cm?
Working:
Answer:
17.An adult ticket costs $30 more than a child's, and 4 adult and 2 child tickets cost $480. With $x an adult ticket and $y a child's: x = y + 30; substituting, 4(y + 30) + 2y = 480, so y = and x = .
Fill in each blank
Working:
Answer:
18.Fen solves x = 4y + 4 and 5x − 3y = 122 by putting x into the second. Which line is right?
- A. 5(4y − 4) − 3y = 122
- B. 20y + 4 − 3y = 122
- C. 5(4y + 4) − 3y = 122
- D. 4y + 4 − 3y = 122
Choose the right answer
Working:
Answer:

Show the answers and working

Solving by substitution worksheet: Answers and working

1. 6
Put y = 2x in: 5x + 2(2x) = 54, 9x = 54, x = 6.
2. −3, 2
7x + 14 = −7, x = −3; back in y = 4x + 14, y = 2.
3. −3
Put y = 4x in: 4x + 1(4x) = −24, 8x = −24, x = −3.
4. 3, −4
Substitute: 2(y + 7) − 5y = 26, so y = −4; back in, x = 3.
5. −3
6(y + 9) + 4y = 24, so 10y = 24 − 6 × (9) and y = −3.
6. 1, 9
In the second, y has coefficient −1; rearranged, y = 4x + 5. Into the first, after a minus, so in brackets: 2x − 4(4x + 5) = −34, giving x = 1 and y = 9.
7. 1, −2
In the second, y has coefficient 1: y = 2 − 4x; into the first, 3x + 3(2 − 4x) = −3, so x = 1 and y = −2.
8. −7
Put x = 4 into the first: 2 × 4 + 3y = 23, so y = 5. Then both into the second: 5 = 3 × 4 + k, so k = −7.

9. A. 5x − 3(4x − 6) = −17
y becomes all of (4x − 6): 5x − 3(4x − 6) = −17.
10. True
Substituting gives x = −2, and y = 4x + 14 gives y = 6. Check the answer in both equations.
11. False
Substituting gives x = 4, and y = 4x − 17 gives y = −1. Check the answer in both equations.
12. C. 8x − 5(3x − 1) = −16
y becomes all of (3x − 1): 8x − 5(3x − 1) = −16.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 11, 55
5y − y = 44, y = 11; x = 5 × 11 = 55.
14. 11 coins
x + y = 20, 10x + 5y = 155. From the first, y = 20 − x; substituting, 10x + 5(20 − x) = 155, so x = 11.
15. 96
x = 5y + 6 and x + y = 114. Substituting, 6y + 6 = 114, so y = 18 and x = 96. It asks for the larger.
16. 12 cm
x = y + 8 and 2x + 2y = 32. Substituting, 2(y + 8) + 2y = 32, so y = 4 and x = 12.
17. 60, 90
4y + 4 × 30 + 2y = 480, so y = 60; x = 60 + 30 = 90.
18. C. 5(4y + 4) − 3y = 122
All of x becomes (4y + 4): 5(4y + 4) − 3y = 122.

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