Equations and inequalities · Ages 13–14
Simultaneous linear equations worksheet
Covers: Solutions of an equation in two unknowns, Solving by graphs, Solving by substitution, Solving by elimination, Simultaneous equations in other forms, From words to simultaneous equations, Word problems with simultaneous equations
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Simultaneous linear equations worksheet
Equations and inequalities · Ages 13–14
Numsprite
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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.
Part A: Working out and filling in (2 marks each)
1.In 3x + 2y = 8, when x = 6, y =
Answer:
2.Write 5x + 3y = 33 as y = − 5x3. When x = 0, y = ; when x = 3, y = .
Fill in each blank
Answer:
3.5x + 4y = 49, x − y = 8. The second gives x = y + 8; put it into the first: y =
Answer:
4.2x − 2y = −14, 3x − y = −3: x = , y =
Fill in each blank
Answer:
5.Multiply both sides of 2x − y = 30 by 2: 4x − 2y =
Answer:
6.4x + 3y = −11, 3x + 5y = 0: x = , y =
Fill in each blank
Answer:
7.x4 + y5 = 1, x − y = −23: x = , y =
Fill in each blank
Answer:
8.x + y6 = x − y5 = −2: x = , y =
Fill in each blank
Answer:
9.A father is 5 times as old as his son. In 3 years he will be 4 times as old. How old is the son now?
Answer:
Part B: Choose, or true or false (2 marks each)
10.The picture shows that x = −2, y = −2 satisfies both ① and ②.
True or false?
Answer:
11.The lines 3x + 2y = 4 and 9x + 6y = 13 never meet.
True or false?
Answer:
12.A has $5 more than B, and they have $35 together. With A's money $x and B's $y, this is x + y = 35 and x − y = 5.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Solve the pair of equations shown by lines ① and ② using the graphs, giving x and y. xy =
Working:
Answer:
14.A father is 28 years older than his son and 3 times as old. With the father x and the son y: x = y + 28 and x = 3y, so 3y = y + 28, y = and x = .
Fill in each blank
Working:
Answer:
15.4 apples and 3 oranges cost $42; 3 apples and 2 oranges cost $30. How much is one apple, in dollars?
Working:
Answer:
16.5 times the sum of two numbers is 125, and 5 times their difference is 75. What is the larger number?
Working:
Answer:
17.4 years ago, A was 2 times as old as B; now their ages add to 47. With A x and B y years old now, which pair of equations is right?
- A. x + y = 47, x + 4 = 2(y + 4)
- B. x + y = 47, x − 4 = 2y − 4
- C. x + y = 47, x − 4 = 2(y − 4)
- D. x + y = 47 − 4, x − 4 = 2(y − 4)
Choose the right answer
Working:
Answer:
18.Chickens and rabbits: 18 heads, 60 legs. With x chickens and y rabbits: x + y = 18 and 2x + 4y = 60. Put the steps of finding the rabbits in order.
- A. 2x + 2y = 36
- B. y = 12
- C. 2y = 24
- D. (2x + 4y) − (2x + 2y) = 60 − 36
Write the letters in the right order
Working:
Answer:
Show the answers and working
Simultaneous linear equations worksheet: Answers and working
Part A: Working out and filling in
1. −5
Put in x = 6: 3 × (6) + 2y = 8, so 2y = −10 and y = −5.
2. 33, 11, 6
Take 5x from both sides, then divide by 3: y = 33 − 5x3. x = 0: 33 − 03 = 11; x = 3: 33 − 153 = 6. Each time x goes up by 3, y goes down by 5.
3. 1
5(y + 8) + 4y = 49, so 9y = 49 − 5 × (8) and y = 1.
4. 2, 9
In the second, y has coefficient −1; rearranged, y = 3x + 3. Into the first, after a minus, so in brackets: 2x − 2(3x + 3) = −14, giving x = 2 and y = 9.
5. 60
Every term is multiplied by 2, the 30 on the right too: 2 × (30) = 60.
6. −5, 3
Multiply each so y's (or x's) coefficients match, subtract to remove it: x = −5, y = 3. Check in both.
7. −8, 15
Multiply the first by 20: 5x + 4y = 20 × (1); with x − y = −23, x = −8 and y = 15.
8. −11, −1
Split it: x + y = 6 × (−2) and x − y = 5 × (−2). Add and halve: x = −11; subtract and halve: y = −1.
9. 9 years old
Father x, son y: x = 5y and x + 3 = 4(y + 3). Substituting, 5y + 3 = 4y + 4 × 3, so y = 9.
Part B: Choose, or true or false
10. True
Only the crossing point, (−2, −2), satisfies both equations.
11. True
The second's x and y coefficients are 3 times the first's. If its constant is 3 times too, they are one line (meeting everywhere); if not, they are parallel (never meeting).
12. True
A has more, so x − y is the positive 5.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. −3
The crossing is (1, −3), so xy = (1) × (−3) = −3.
14. 14, 42
3y − y = 28, y = 14; x = 3 × 14 = 42.
15. 6 dollars
4x + 3y = 42 and 3x + 2y = 30. The first times 2, the second times 3; subtract to remove y: x = 6.
16. 20
5(x + y) = 125 and 5(x − y) = 75: divide by 5 and by 5 for x + y and x − y, then add and halve: x = 20.
17. C. x + y = 47, x − 4 = 2(y − 4)
Now: x + y = 47; 4 years ago, A was x − 4 and B y − 4: x − 4 = 2(y − 4).
18. A → D → C → B
Double the first, take it from the second to remove x, then halve.
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