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Simultaneous Equations

Description: Linear equations
Number of Questions: 15
Created by:
Tags: Linear equations Solving a Pair of Linear Equations
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Find 'a' if x + ay = 3 has a solution (3, 1).

  1. 0

  2. 1

  3. 2

    • 1

  5. None of these

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Correct Option: A
Explanation:

Substitute values of x, y in the equation. 3 + a = 3 Or a = 0

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

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Correct Option: B
Explanation:

Substitute x = 3 - 2y in the second equation.  

6 - 4y + y = 3 Or y = 1 And x = 1

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

Show answer
Correct Option: C
Explanation:

From first equation, y = (7 - 3x)/2

Substitute in second: 2x - (21 - 9x)/2 = -4 13x = 13 Or x = 1 

Substitute in the first equation to get y = 2.

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

Show answer
Correct Option: D
Explanation:

From the second equation, y = 1 - x Substituting this in the first equation, we get 2x - 3 + 3x = - 3 Or x = 0 And y = 1

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

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Correct Option: B
Explanation:

Let the two numbers be x and y. xy = 72 And x/y = 18 On dividing the two equations, we get y^2 = 4 Or y = 2 Substituting the value of y = 2 in either of the equations, we get x = 36

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

  1. (0, 0)

  2. (1, 0)

  3. (3, 2)

  4. Infinite solutions

  5. None of these

Show answer
Correct Option: D
Explanation:

As both the lines are same, all the points lying on the line will be the solution. As the lines are same, so there are infinite solutions.

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

Show answer
Correct Option: C
Explanation:

The equations are as follows:

2x + 3y = 60 and 3x + 2y = 50 Adding both the equations, we get 5x + 5y = 110 or x + y = 22 Subtracting both the equations, we get -x + y = 10

y = 16 and x = 6

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

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Correct Option: A
Explanation:

x + y = 25 and x - y = 13 (where x is bigger)

On adding the two equations, we get 2x = 28 or x = 14 And y = 11

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

Show answer
Correct Option: B
Explanation:

Let x and y be the two speeds. y = x + 20 Time taken for up trip = 600/x Time taken for return = 600/(x + 20) Difference = 8 hours Or 12000 = 8x(x + 20)x = 30 y = 50

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

Show answer
Correct Option: B
Explanation:

Let l and w be the length and the width, respectively. lw = 120 And (l + 2)(w - 4) = 84 Substituting w = 120/l, we get (l + 2)(120 - 4l) = 84l Or l = 12 cm

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

Show answer
Correct Option: C
Explanation:

Substitute 1/x = a and 1/y = ba + b = 5/6 and a - b = 1/6. Hence, a = 1/2 and b = 1/3 And x = 2 and y = 3

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

Show answer
Correct Option: C
Explanation:

Multiply the first equation by 'a' and subtract from second. (b - a)y = b - a Or y = 1 and x = 1

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

Show answer
Correct Option: D
Explanation:

Let the number of marbles with A and B be x and y, respectively. x - 1 = y + 1 and x + 1 = 2(y - 1)

On solving, we get y = 5 and x = 7

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

Show answer
Correct Option: D
Explanation:

The two lines have equal slope, but different intercepts. Hence, parallel.

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

  1. (1, 2)

  2. (3, 1)

  3. (2, 1)

  4. (1, 0)

  5. None of these

Show answer
Correct Option: A
Explanation:

Subtract to get 3y = 6 Or y =2 Plug in to get x = 1

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