Equations and inequalities · Ages 13–14

Solutions of an equation in two unknowns worksheet

Part of: Simultaneous linear equations

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Equations and inequalities · Ages 13–14

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

1.In 2x + 4y = 30, when x = 3, y =
Answer:
2.2x + 4y = 8: when x = 0, y = ; when y = 0, x = .
Fill in each blank
Answer:
3.In 2x − y = −18, when y = 8, x =
Answer:
4.Write 2x + 4y = 14 as y = − 2x4. When x = 1, y = ; when x = 5, y = .
Fill in each blank
Answer:
5.Write 2x + 4y = 40 as y = − 2x4. When x = 4, y = ; when x = 8, y = .
Fill in each blank
Answer:

6.Which point lies on the line x + 2y = −4?
- A. (4, −4)
- B. (−4, 4)
- C. (5, −4)
- D. (4, −5)
Choose the right answer
Answer:
7.(5, 3) is a solution of x + 4y = 17.
True or false?
Answer:
8.Which point lies on the line 3x + y = 19?
- A. (6, 1)
- B. (7, 1)
- C. (1, 6)
- D. (6, 0)
Choose the right answer
Answer:
9.(1, −2) is a solution of 4x + 4y = −4.
True or false?
Answer:
10.From 9x + y = −20, it follows that y = −20 − 10x.
True or false?
Answer:
11.(x, y) = (−4, −3) solves which of these equations?
- A. 2x − 3y = −17
- B. 2x + 3y = −17
- C. 2x + 3y = −14
- D. 3x + 2y = −17
Choose the right answer
Answer:
12.Which of these points is not on the line x + 5y = 29?
- A. (9, 6)
- B. (4, 5)
- C. (−1, 6)
- D. (9, 4)
Choose the right answer
Answer:

13.Exactly $52 buys x pens at $6 each and y notebooks at $2 each: 6x + 2y = 52. With 4 pens, that is notebooks; with 6 pens, notebooks.
Fill in each blank
Working:
Answer:
14.An isosceles triangle's perimeter is 34 cm, each equal side x cm and the base y cm: 2x + y = 34. When the base is 2 cm, how long is each equal side, in cm?
Working:
Answer:
15.13 sweets are all shared between two brothers, at least 1 each, the elder getting more. With x for the elder and y for the younger: x + y = 13. How many ways are there?
Working:
Answer:
16.Exactly $92 buys stamps at $3 and at $8, at least one of each: 3x + 8y = 92. At most how many $8 stamps can be bought?
Working:
Answer:
17.A rectangle's perimeter is 48 cm, x cm long and y cm wide: 2x + 2y = 48. When it is 15 cm long, it is cm wide; if it is a square, its side is cm.
Fill in each blank
Working:
Answer:
18.Exactly $54 buys x boxes of chocolates at $3 and y bags of sweets at $4: 3x + 4y = 54. Which of these could (x, y) be?
- A. (22, −3)
- B. (6, 9)
- C. (9, 6)
- D. (7, 9)
Choose the right answer
Working:
Answer:

Show the answers and working

Solutions of an equation in two unknowns worksheet: Answers and working

1. 6
Put in x = 3: 2 × (3) + 4y = 30, so 4y = 24 and y = 6.
2. 2, 4
x = 0: 4y = 8, y = 2; y = 0: 2x = 8, x = 4. These two points draw the line most easily.
3. −5
Put in y = 8: 2x − 1 × (8) = −18, so 2x = −10 and x = −5.
4. 14, 3, 1
Take 2x from both sides, then divide by 4: y = 14 − 2x4. x = 1: 14 − 24 = 3; x = 5: 14 − 104 = 1. Each time x goes up by 4, y goes down by 2.
5. 40, 8, 6
Take 2x from both sides, then divide by 4: y = 40 − 2x4. x = 4: 40 − 84 = 8; x = 8: 40 − 164 = 6. Each time x goes up by 4, y goes down by 2.

6. A. (4, −4)
A point is on the line when its coordinates solve the equation: 1 × (4) + 2 × (−4) = −4.
7. True
Put in x = 5, y = 3: 1 × (5) + 4 × (3) = 17. It is a solution only if that equals 17.
8. A. (6, 1)
A point is on the line when its coordinates solve the equation: 3 × (6) + 1 × (1) = 19.
9. True
Put in x = 1, y = −2: 4 × (1) + 4 × (−2) = −4. It is a solution only if that equals −4.
10. False
Take 9x from both sides: y = −20 − 9x. With y written in x, each x gives one y, ready for a table.
11. B. 2x + 3y = −17
Put x = −4, y = −3 into each: only 2x + 3y gives −17.
12. A. (9, 6)
Put each point in: only (9, 6) makes the left side something other than 29. Along the line, when x goes up by 5, y goes down by 1, not up.

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

13. 14, 8
With x = 4: 2y = 52 − 6 × 4, y = 14; with x = 6: y = 8. One equation in two unknowns has many solutions.
14. 16 cm
Put in y = 2: 2x + 2 = 34, 2x = 34 − 2, x = 16.
15. 6 ways
y starts at 1, and x > y means y < 13 ÷ 2: y can be 1 to 6, so 6 ways.
16. 10 stamps
The more y, the fewer x; the least x can be is 4 (another 8 fewer is no longer positive): 3 × 4 + 8y = 92, y = 10.
17. 9, 12
2 × 15 + 2y = 48, y = 9; a square has x = y: 4x = 48, x = 12.
18. B. (6, 9)
3 × 6 + 4 × 9 = 54, and x and y are whole and positive, as the story needs.

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