Equations and inequalities · Ages 13–14

Solving by elimination worksheet

Part of: Simultaneous linear equations

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Equations and inequalities · Ages 13–14

Numsprite
numsprite.com

Name:Date:Score:／48

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

1.4x + y = 9, 5x − y = 9. Adding them: x = , so x = .
Fill in each blank
Answer:
2.x + 4y = −13, 4x − 4y = 28. Adding them: x = , so x = .
Fill in each blank
Answer:
3.Multiply both sides of 6x − y = 27 by 4: 24x − 4y =
Answer:
4.4x − 4y = 28, 3x + y = 9: x = , y =
Fill in each blank
Answer:
5.4x + 3y = 19, 3x − 2y = −24, y =
Answer:
6.5x + 4y = −13, 2x + 3y = −1: x = , y =
Fill in each blank
Answer:
7.3x + 5y = −4, 5x − 3y = −18, y =
Answer:
8.5x + 2y = −21, 3x + 3y = −9: x = , y =
Fill in each blank
Answer:

9.4x + 2y = −6 and 2x − 2y = −6. How do you eliminate y?
- A. Double the first, then add
- B. Subtract one from the other
- C. Add the two
- D. y can't be eliminated
Choose the right answer
Answer:
10.x + y = 2 and 5x − y = −8. How do you eliminate y?
- A. y can't be eliminated
- B. Add the two
- C. Double the first, then add
- D. Subtract one from the other
Choose the right answer
Answer:
11.① x + 2y = 5, ② 4x + y = 6. Multiplying ① by 4 and taking away ② eliminates x.
True or false?
Answer:
12.① x + 5y = 7, ② 3x + y = 7. Multiplying ① by 2 and taking away ② eliminates x.
True or false?
Answer:

13.① 5x + 2y = 13, ② 2x + 4y = 2. To eliminate x, what should ① and ② each be multiplied by?
- A. ① × 5, ② × 2
- B. ① × 4, ② × 2
- C. ① × 2, ② × 5
- D. ① × 2, ② × 1
Choose the right answer
Working:
Answer:
14.4 apples and 5 oranges cost $81; 5 apples and 1 oranges cost $54. How much is one apple, in dollars?
Working:
Answer:
15.Solve 2x + 4y = 16 and 5x − 4y = −2. Put the steps of eliminating in order.
- A. y = 3
- B. (2x + 4y) + (5x − 4y) = 16 − 2
- C. x = 2
- D. 7x = 14
Write the letters in the right order
Working:
Answer:
16.3 pens and 1 notebooks cost $31; 1 pens and 3 notebooks cost $45. How much are one pen and one notebook together, in dollars?
Working:
Answer:
17.A boat goes 48 km downstream in 4 hours and back upstream in 12 hours. With u km/h its speed in still water and v km/h the current's: u + v = , u − v = , so u = .
Fill in each blank
Working:
Answer:
18.2 adult and 3 child tickets cost $295; 2 adult and 2 child tickets cost $250. Subtracting: y = , so a child's ticket is $.
Fill in each blank
Working:
Answer:

Show the answers and working

Solving by elimination worksheet: Answers and working

1. 9, 18, 2
+y and −y cancel: (4 + 5)x = 9 + (9), 9x = 18, x = 2.
2. 5, 15, 3
+4y and −4y cancel: (1 + 4)x = −13 + (28), 5x = 15, x = 3.
3. 108
Every term is multiplied by 4, the 27 on the right too: 4 × (27) = 108.
4. 4, −3
Multiply the second by 4 so y's coefficients match in size, then add or subtract: x = 4; back in, y = −3.
5. 9
To eliminate x: the first times 3, the second times 4, both x coefficients 4 × 3; subtract, and y = 9.
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. 1
To eliminate x: the first times 5, the second times 3, both x coefficients 3 × 5; subtract, and y = 1.
8. −5, 2
Multiply each so y's (or x's) coefficients match, subtract to remove it: x = −5, y = 2. Check in both.

9. C. Add the two
Same coefficient: subtract; opposite: add. Either way y is gone.
10. B. Add the two
Same coefficient: subtract; opposite: add. Either way y is gone.
11. True
① × 4 has x coefficient 4 × 1; it must equal ②'s 4 for x to go.
12. False
① × 2 has x coefficient 2 × 1; it must equal ②'s 3 for x to go.

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

13. C. ① × 2, ② × 5
① × 2 and ② × 5 make both x coefficients 5 × 2; subtracting removes x.
14. 9 dollars
4x + 5y = 81 and 5x + y = 54. The first times 1, the second times 5; subtract to remove y: x = 9.
15. B → D → C → A
y's coefficients are opposite, so add to remove y and find x; then put it back for y.
16. 19 dollars
Add them: 4x + 4y = 31 + 45; divide by 4: x + y = 19. No need to find each.
17. 12, 4, 8
Downstream speed = 48 ÷ 4 = 12, upstream = 48 ÷ 12 = 4. Adding: 2u = 12 + 4, u = 8.
18. 1, 45, 45
The adult tickets are the same number, so subtracting removes x: (3 − 2)y = 295 − 250, y = 45.

Numsprite · numsprite.com/en/worksheets/simultaneous-linear-equations/elimination-method