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Simultaneous Equations

Solving simultaneous linear equations using substitution, elimination, and application to word problems including speed/distance, geometry, and system identification (consistent/dependent/inconsistent)

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Find 'a' if x + ay = 3 has a solution (3, 1).

  1. 0
  2. 1
  3. 2
  4. - 1
  5. None of these
Question 2 Multiple Choice (Single Answer)

Solve: x + 2y = 3 and 2x + y = 3

  1. x = 1, y = 0
  2. x = 1, y = 1
  3. x = 2, y = 1/2
  4. No solution exists for this set.
  5. None of these
Question 3 Multiple Choice (Single Answer)

Solve using elimination method: 3x + 2y = 7 and 2x - 3y = - 4

  1. (1, 0)
  2. (0, 2)
  3. (1, 2)
  4. (3, 4)
  5. None of these
Question 4 Multiple Choice (Single Answer)

Find the solution to the equation 2x - 3y = - 3 and x + y = 1 using substitution method.

  1. (1, 2)
  2. (3, 1)
  3. (1, 0)
  4. (0, 1)
  5. None of these
Question 5 Multiple Choice (Single Answer)

Two positive numbers, when multiplied, give 72 and when the smaller number divides the greater, the quotient is 18. Find the smaller number.

  1. 18
  2. 2
  3. 22
  4. 20
  5. None of these
Question 6 Multiple Choice (Single Answer)

Solve: 5x - 9y = 2 and 10x - 18y = 4

  1. (0, 0)
  2. (1, 0)
  3. (3, 2)
  4. Infinite solutions
  5. None of these
Question 7 Multiple Choice (Single Answer)

A purchases 2 pencils and 3 pens. The cost was 60 dollars. His friend purchsed 3 pencils and 2 pens. The cost was 50 dollars. Find the cost of each pencil and pen.

  1. $9 and $16
  2. $6 and $15
  3. $6 and $16
  4. $8 and $16
  5. None of these
Question 8 Multiple Choice (Single Answer)

Two numbers when added give 25 and the difference between them is 13. Find the greater number.

  1. 14
  2. 11
  3. 20
  4. 22
  5. None of these
Question 9 Multiple Choice (Single Answer)

A train covers 600 km in a certain time. While coming back, it increases its speed by 20 km and completes the journey in 8 hours less. Find the two speeds.

  1. 20, 50
  2. 30, 50
  3. 30, 45
  4. 35, 40
  5. None of these
Question 10 Multiple Choice (Single Answer)

A rectangle has area of 120 sq. cm. When the length increases by 2 and the width decreases by 4, the new area is 84 sq. cm. Find the original length.

  1. 10 cm
  2. 12 cm
  3. 13 cm
  4. 15 cm
  5. None of these
Question 11 Multiple Choice (Single Answer)

Solve: 1/x + 1/y = 5/6 and 1/x - 1/y = 1/6

  1. (- 2, - 3)
  2. (1/2, 1/3)
  3. (2, 3)
  4. (3, 2)
  5. None of these
Question 12 Multiple Choice (Single Answer)

Solve: x + y = 2 and ax + by = a + b

  1. (a, 1)
  2. (a, b)
  3. (1, 1)
  4. (1, b)
  5. None of these
Question 13 Multiple Choice (Single Answer)

A and B had some marbles. If A gives 1 to B, then both have equal number of marbles. If B gives 1 to A, then A has two more marbles as compared to B. Find the numbers of marbles with A and B, respectively.

  1. 9, 7
  2. 7, 6
  3. 6, 5
  4. 7, 5
  5. None of these
Question 14 Multiple Choice (Single Answer)

Find solution of the equations: x + 2y = 4 and 2x + 4y = 12

  1. (1, 1)
  2. (2, 1)
  3. (0, 0)
  4. No solution as the lines are parallel
  5. Infinite solutions
Question 15 Multiple Choice (Single Answer)

Solve: x + 2y = 5 and x - y = - 1

  1. (1, 2)
  2. (3, 1)
  3. (2, 1)
  4. (1, 0)
  5. None of these
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