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Important Questions: Pair of Linear Equations in Two Variables - Class 10 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 10 - Important Questions: Pair of Linear Equations in Two Variables

Important Questions: Pair of Linear Equations in Two Variables for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Important Questions: Pair of Linear Equations in Two Variables questions and answers have been prepared according to the Class 10 exam syllabus.The Important Questions: Pair of Linear Equations in Two Variables MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Important Questions: Pair of Linear Equations in Two Variables below.
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Important Questions: Pair of Linear Equations in Two Variables - Question 1

If a pair of linear equations has infinitely many solutions, then the lines representing them will be

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 1

If two lines i.e. a pair of linear equations, has infinitely many solutions it means lines are overlapping each other i.e. coincident lines.

Important Questions: Pair of Linear Equations in Two Variables - Question 2

The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 2

a1 / a2 = b1 / b2 = c1 / c2
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2 
When these are equal then it is consistent.
Therefore option (C) is correct .

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Important Questions: Pair of Linear Equations in Two Variables - Question 3

If am ≠ bl, then the system of equations, ax + by = c, lx + my = n

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 3

If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.

Given,

Pair of lines represented by the equations

ax + by = c

lx + my = n

For unique solution

For infinite solutions

For no solution

Given,

This can be transformed into

Therefore, If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.

Important Questions: Pair of Linear Equations in Two Variables - Question 4

The pair of equations y = 0 and y = - 7 has

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 4

The equation are y=0 and y=-7
y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0
The line will be parallel
if we try to solve these equations we get 0=7 which is absurd.
So the equations are inconsistent.
Therefore there is no solution.

Important Questions: Pair of Linear Equations in Two Variables - Question 5

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. The present ages (in years) of the son and the father are, respectively. 

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 5

Let the present age of father's be x years and present age of son's be y years.

According to the problem
x = 6y 
After 4 years
x + 4 = 4(y + 4)
Hence we get two equations
x = 6y ...(1)
x + 4 = 4(y + 4) ...(2)
Simplifying eq (2)
x + 4 = 4y + 16
x - 4y = 12
Put x = 6y in eq(2), we get
6y - 4y = 12
2y = 12
y = 6 years
and x = 6y = 36 years
Present age of son = 6 years
and present age of father = 36 years

Important Questions: Pair of Linear Equations in Two Variables - Question 6

The pair of equations x = a and y = b graphically represents lines which are

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 6

By graphically in every condition, if a, b>>0; a, b< 0, a>0, b< 0; a<0, b>0 but a = b≠ 0.
The pair of equations x = a and y = b graphically represents lines which are intersecting at (a, b).
If a, b > 0 

Similarly, in all cases two lines intersect at (a, b).

Important Questions: Pair of Linear Equations in Two Variables - Question 7

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of the number gets reversed. The number is

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 7

Lets,

First digit number = x

Second digit number = y

Number = (x+10y)

A/Q,

x + y = 9 ...................... (i)

A/Q,

(x+10y) = (10x+y) + 27

x + 10y = 10x + y +27

9x - 9y = 27

9(x - y) = 27

x - y = 27/9

x - y = 3 ......................... (ii)

Equation (i) and (ii) we get,

x = 3

Putting the value of x in eq.(i)

we get,

y = 6

Number = (10x +y)

= 10 x 3 + 6

= 30 + 6

= 36

Important Questions: Pair of Linear Equations in Two Variables - Question 8

Match the Column:

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 8

Important Questions: Pair of Linear Equations in Two Variables - Question 9

If x = a, y = b is the solution of the pair of equations x - y = 2 and x + y = 4, then the respective values of a and b are

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 9

Important Questions: Pair of Linear Equations in Two Variables - Question 10

A pair of linear equations which has a unique solution x = 2, y = - 3 is

Detailed Solution for Important Questions: Pair of Linear Equations in Two Variables - Question 10

x - 4y -14 = 0

x = 4y+14

putting this in 5x - y -13 = 0

5(4y+14) - y -13 =0

19y = -57     

y = -3

putting y = -3 in x = 4y+14

x = 4(-3)+14

x = 2

so option b is correct

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