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Grade 8 · Math

Solve a pair of linear equations

Find and check the ordered pair that satisfies two linear equations.

6 authored questions + worked example

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Worked example

Which ordered pair (x, y) solves both equations: x + y = 5 and x − y = -1?

Answer & why

Answer: (2, 3)

Add the equations to eliminate y: 2x = 4, so x = 2. Substitute into x + y = 5 to get y = 3. The pair (2, 3) satisfies both equations.

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All questions

All 6 authored questions for this skill.

Question 1

Which ordered pair (x, y) solves both equations: x + y = 7 and x − y = 3?

  1. (5, 3)
  2. (5, 2)
  3. (2, 5)
  4. (6, 2)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (5, 2)

Add the equations to eliminate y: 2x = 10, so x = 5. Substitute into x + y = 7 to get y = 2. The pair (5, 2) satisfies both equations.

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Question 2

Which ordered pair (x, y) solves both equations: x + y = 9 and x − y = -3?

  1. (4, 6)
  2. (3, 7)
  3. (6, 3)
  4. (3, 6)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (3, 6)

Add the equations to eliminate y: 2x = 6, so x = 3. Substitute into x + y = 9 to get y = 6. The pair (3, 6) satisfies both equations.

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Question 3

Which ordered pair (x, y) solves both equations: x + y = 11 and x − y = 3?

  1. (4, 7)
  2. (8, 4)
  3. (7, 5)
  4. (7, 4)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (7, 4)

Add the equations to eliminate y: 2x = 14, so x = 7. Substitute into x + y = 11 to get y = 4. The pair (7, 4) satisfies both equations.

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Question 4

Which ordered pair (x, y) solves both equations: x + y = 8 and x − y = 4?

  1. (6, 2)
  2. (2, 6)
  3. (6, 3)
  4. (7, 2)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (6, 2)

Add the equations to eliminate y: 2x = 12, so x = 6. Substitute into x + y = 8 to get y = 2. The pair (6, 2) satisfies both equations.

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Question 5

Which ordered pair (x, y) solves both equations: x + y = 5 and x − y = -1?

  1. (2, 4)
  2. (2, 3)
  3. (3, 3)
  4. (3, 2)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (2, 3)

Add the equations to eliminate y: 2x = 4, so x = 2. Substitute into x + y = 5 to get y = 3. The pair (2, 3) satisfies both equations.

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Question 6

Which ordered pair (x, y) solves both equations: x + y = 5 and x − y = 3?

  1. (4, 1)
  2. (1, 4)
  3. (4, 2)
  4. (5, 1)
A hint

A system’s solution must satisfy both equations, not just one.

Answer & why

Answer: (4, 1)

Add the equations to eliminate y: 2x = 8, so x = 4. Substitute into x + y = 5 to get y = 1. The pair (4, 1) satisfies both equations.

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