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Test: Pair of Linear Equations in Two Variables (Medium) - Class 10 MCQ


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19 Questions MCQ Test Extra Documents, Videos & Tests for Class 10 - Test: Pair of Linear Equations in Two Variables (Medium)

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Test: Pair of Linear Equations in Two Variables (Medium) - Question 1
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If the lines given by

3x + 2ky = 2

2x + 5y + 1 = 0

are parallel, then the value of k is

Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 1
For parallel lines

Test: Pair of Linear Equations in Two Variables (Medium) - Question 2
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The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is

Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 2

For infinitely many solutions

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Test: Pair of Linear Equations in Two Variables (Medium) - Question 3
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Solve for x and y, if x + y = 7and 2x + 3y = 18.

Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 3
2x + 3y = 18 .......... (1)

x + y = 7 ......... (2)

Multiplying equation (2) by 2, we get

2x + 2y = 14 ........ (3)

Subtracting (3) from (2), we get

y = 4

Using this in x + y = 7, we have

x + 4 = 7

or x = 7 − 4 = 3

Test: Pair of Linear Equations in Two Variables (Medium) - Question 4
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One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. The second equation can be
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 4
For dependent pair, the two lines must have

a1 / a2 = b1 / b2 = c1 / c2​ ​

For option (d)

a1 / a2 = b1 / b2 = c1 / c2​ ​= -1 / 2

Test: Pair of Linear Equations in Two Variables (Medium) - Question 5
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Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Then the numbers are:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 5
According to given information

Test: Pair of Linear Equations in Two Variables (Medium) - Question 6
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The solution of the equations x – y = 2 and x + y = 4 is:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 6
Adding both equations, we have

Test: Pair of Linear Equations in Two Variables (Medium) - Question 7
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For which values of a and b, will the following pair of linear equations have infinitely many solutions?

x + 2y = 1

(a – b)x + (a + b)y = a + b – 2
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 7
For infinitely many solutions

Test: Pair of Linear Equations in Two Variables (Medium) - Question 8
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The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 8
Let the age of father be x and of son is y.

Then according to question,

x = 6y …..(i)

Four years hence age of son will be y + 4 and age of father will be x + 4

Then according to question,

x + 4 = 4 (y + 4)

x – 4y = 12 …..(ii)

Solving equations (i) and (ii) we get:

y = 6 and x = 36

Test: Pair of Linear Equations in Two Variables (Medium) - Question 9
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Rakshita has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Rs.1 andRs.2 coins is, respectively
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 9
Let her number of Rs.1 coins are x

Let the number of Rs.2 coins are y

Then

By the given conditions x + y = 50 …..(i)

1 × x + 2 × y = 75 ⇒ x + 2y = 75 …..(ii)

Solving equations (i) and (ii) we get:

(x + 2y) – (x + y) = 75 – 50 ⇒ y = 25

Therefore, x = 50 – 25 = 25

So the number of coins are 25, 25 each.

Test: Pair of Linear Equations in Two Variables (Medium) - Question 10
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In a competitive examination, one mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 10
Let x be the number of correct answers of the questions in a competitive exam.

Then, 120 − x be the number of wrong answers

Then by given condition

Test: Pair of Linear Equations in Two Variables (Medium) - Question 11
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The angles of a cyclic quadrilateral ABCD are:

∠A = (6x + 10)0, ∠B = (5x)0

∠C = (x + y)0, ∠D = (3y - 10)0

Then value of x and y are:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 11
In cyclic quadrilateral, sum of opposite angles is 1800

Therefore

6x + 10 + x + y = 180

⇒ 7x + y = 170 …..(i)

5x + 3y – 10 = 180

⇒ 5x + 3y = 190 …..(ii)

Multiplying equations (i) and (ii), we get:

x = 20o and y = 30o

Test: Pair of Linear Equations in Two Variables (Medium) - Question 12
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A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Reema paid Rs. 22 for a book kept for six days, while Ruchika paid Rs 16 for the book kept for four days, then the charge for each extra day is:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 12
Let Rs. x be the fixed charge and Rs. y be the charge for each extra day.

Then by the given conditions

x + 4y = 22 …..(i)

x + 2y = 16 …..(ii)

Subtracting equation (ii) from (i), we get:

y = Rs. 3

Test: Pair of Linear Equations in Two Variables (Medium) - Question 13
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Aruna has only Re. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Re. 1 and Rs. 2 coins are respectively
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 13
Let number of Re.1 coin = x

Number of Re. 2 coin = y

A / q,

x + y = 50 ..............................(i)

x + 2y = 75 ..............................(ii)

On Solving eqn. (i) and (ii), we get

x = 25 and y = 25

Test: Pair of Linear Equations in Two Variables (Medium) - Question 14
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The pair of equations x = a and y = b graphically represents lines which are
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 14
The equations are x = a and y = b.

The graph of x = a is a line parallel to y-axis and y = b is a line parallel to x-axis.

∴ The angle between them is 90o , i.e. they intersect.

So, the equations are consistent.

Now solving simultaneously, the solution is (a, b).

So, the point of intersection is (a, b).

Test: Pair of Linear Equations in Two Variables (Medium) - Question 15
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The value of k, for which equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution is
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 15
For a system of equations a1x + b1y + c1 ​= 0; a2x + b2y + c2 = 0 to have non-zero solutions, the condition to be satisfied is

a1 / a2 = b1 / b2 = c1 / c2​ ​

∴ 3 / k = 5 / 10 ​

or k = 6

Test: Pair of Linear Equations in Two Variables (Medium) - Question 16
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Two equations in two variables taken together are called
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 16
Two linear equations in two variables taken together are called simultaneous linear equations. The solution of system of simultaneous linear equation is the ordered pair (x, y) which satisfies both the linear equations.
Test: Pair of Linear Equations in Two Variables (Medium) - Question 17
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The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 17
a1 / a2 = 1 / -4

b1 / b2 = 2 / -8 = 1 / -4

c1 / c2 = -5 / 20 = -1 / 4

This shows:

a1 / a2 = b1 / b2 = c1 / c2

Therefore, the pair of equations has infinitely many solutions.

Test: Pair of Linear Equations in Two Variables (Medium) - Question 18
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If a pair of linear equations is consistent, then the lines are:
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 18
Because the two lines definitely have a solution.
Test: Pair of Linear Equations in Two Variables (Medium) - Question 19
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The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
Detailed Solution for Test: Pair of Linear Equations in Two Variables (Medium) - Question 19
Given, 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0

a1 / a2 = 9 / 18 = 1 / 2

b1 / b2 = 3 / 6 = 1 / 2

c1 / c2 = 12 / 26 = 6 / 13

Since, a1 / a2 = b1 / b2 ≠ c1 / c2

So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

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