Equations and inequalities · Ages 13–14

Simultaneous equations in other forms 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.x + y = 3x − y = −6: x = , y =
Fill in each blank
Answer:
2.2x + y = 6x − y = −4: x = , y =
Fill in each blank
Answer:
3.x4 + y3 = 3, x − y = −16: x = , y =
Fill in each blank
Answer:
4.4(x + 3) + y = 5, x + 4(y − 6) = −37: x = , y =
Fill in each blank
Answer:
5.2(x + 3) + y = 10, x + 3(y − 6) = −11: x = , y =
Fill in each blank
Answer:
6.x5 + y4 = 3, x − y = 6: x = , y =
Fill in each blank
Answer:
7.x + y5 = x − y6 = 6: x = , y =
Fill in each blank
Answer:
8.2x + y = −8 and 8x + 4y = have endlessly many solutions. What number goes in the box?
Answer:

9.How many solutions do 3x + 2y = 3 and 9x + 6y = 12 have together?
- A. None
- B. Two
- C. Endlessly many
- D. Exactly one
Choose the right answer
Answer:
10.How many solutions do 4x + 3y = 1 and 15x + 9y = 3 have together?
- A. Two
- B. None
- C. Endlessly many
- D. Exactly one
Choose the right answer
Answer:
11.Multiplying both sides of x3 + y6 = 3 by 18 gives 6x + 3y = 3.
True or false?
Answer:
12.Multiplying both sides of x6 + y3 = 4 by 18 gives 3x + 6y = 4.
True or false?
Answer:

13.Solve x4 + y2 = 8 and y = x − 8. Put the steps in order.
- A. x = 16
- B. x4 + y2 = 8
- C. 2x + 4y = 64
- D. 2x + 4(x − 8) = 64
Write the letters in the right order
Working:
Answer:
14.12 of A's money and 14 of B's make $16, and A has $2 more than B. x2 + y4 = 16, x − y = 2: A has $ and B $.
Fill in each blank
Working:
Answer:
15.If 3x + 2y = 11 and kx + 6y = 34 have no solution, what is k?
Working:
Answer:
16.The three expressions x + 3y, 9x − y and 7 all have the same value. x = , y =
Fill in each blank
Working:
Answer:
17.2 times the sum of two numbers is 86, and 3 times their difference is 51. What is the larger number?
Working:
Answer:
18.Company A charges C = 12n + 80 and company B C = 12n + 80 (n hours, C dollars). When do the two charge the same?
- A. Never
- B. At exactly two values of n
- C. For every n
- D. At exactly one n
Choose the right answer
Working:
Answer:

Show the answers and working

Simultaneous equations in other forms worksheet: Answers and working

1. −3, −3
Split it into two: x + y = −6 and 3x − y = −6; adding removes y: x = −3, y = −3.
2. −1, −2
Split it into two: 2x + y = −4 and 6x − y = −4; adding removes y: x = −1, y = −2.
3. −4, 12
Multiply the first by 12: 3x + 4y = 12 × (3); with x − y = −16, x = −4 and y = 12.
4. −1, −3
Open the brackets and tidy into ax + by = c, then eliminate: x = −1, y = −3.
5. 1, 2
Open the brackets and tidy into ax + by = c, then eliminate: x = 1, y = 2.
6. 10, 4
Multiply the first by 20: 4x + 5y = 20 × (3); with x − y = 6, x = 10 and y = 4.
7. 33, −3
Split it: x + y = 5 × (6) and x − y = 6 × (6). Add and halve: x = 33; subtract and halve: y = −3.
8. −32
Endlessly many means one line: the second is the first times 4, so the right side is 4 × (−8) = −32.

9. A. None
Compare: x and y coefficients out of proportion, one solution; in proportion but the constant not, none; all in proportion, endlessly many.
10. D. Exactly one
Compare: x and y coefficients out of proportion, one solution; in proportion but the constant not, none; all in proportion, endlessly many.
11. False
Every term is multiplied by 18, the 3 on the right too: 6x + 3y = 18 × 3.
12. False
Every term is multiplied by 18, the 4 on the right too: 3x + 6y = 18 × 4.

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

13. B → C → D → A
Clear the fractions by multiplying by 4 × 2, substitute y = x − 8, then solve for x.
14. 22, 20
Times 2 × 4 clears the first's fractions; with x − y = 2: x = 22, y = 20.
15. 9
No solution means parallel lines: the coefficients are in proportion. 6 is 3 times 2, so k = 3 × 3 = 9; and 34 isn't 3 times 11, so they don't coincide.
16. 1, 2
That is x + 3y = 9x − y = 7: split into x + 3y = 7 and 9x − y = 7, giving x = 1, y = 2.
17. 30
2(x + y) = 86 and 3(x − y) = 51: divide by 2 and by 3 for x + y and x − y, then add and halve: x = 30.
18. C. For every n
Compare: different hourly rates cross once; the same rate with different basic fees are parallel; all the same, they coincide.

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