# Class 10

Explore popular questions from Pair of Linear Equations in Two Variables for Class 10. This collection covers Pair of Linear Equations in Two Variables previous year Class 10 questions hand picked by experienced teachers.

## Mathematics

Pair of Linear Equations in Two Variables

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Q 1. The pair of equations {tex} 3 ^ { x + y } = 81,81 ^ { x - y } = 3 {/tex} has

A

no solution

B

the solution {tex} x = 2 ^ { 1 / 2 } , y = 2 ^ { 1 / 2 } {/tex}

C

the solution {tex} x = 2 , y = 2 {/tex}

the solution {tex} x = 2 \frac { 1 } { 8 } , y = 1 \frac { 7 } { 8 } {/tex}

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Q 2. The condition for which the system of equations {tex} \mathrm { k } x - \mathrm { y } = 2 {/tex} and {tex} 6 x - 2 \mathrm { y } = 3 {/tex} has a unique solution is

A

{tex} \mathrm{k = 3} {/tex}

{tex} \mathrm {k \neq 3} {/tex}

C

{tex} \mathrm { k } \neq 0 {/tex}

D

{tex} \mathrm{k = 0} {/tex}

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Q 3. The equations {tex} a x + b = 0 {/tex} and {tex} c x + d = 0 {/tex} are consistant if

{tex} a d = b c {/tex}

B

{tex} a d + b c = 0 {/tex}

C

{tex} a b - c d = 0 {/tex}

D

{tex} a b + c d = 0 {/tex}

##### Explanation

ax+b=0, cx+d=0 are consistent if a/c=b/d

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Q 4. The solution to the system of equation {tex} | x + y | = 1 {/tex} and {tex} x - y = 0 {/tex} is given by

A

{tex} x = y = 1 / 2 {/tex}

B

{tex} x = y = - 1 / 2 {/tex}

C

{tex} x = 1 , y = 0 {/tex}

{tex} x = \mathrm { y } = 1 / 2 {/tex} or {tex} x = \mathrm { y } = - 1 / 2 {/tex}

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Q 5. The value of {tex} x + y {/tex} in the solution of equations {tex} \frac { x } { 4 } + \frac { y } { 3 } = \frac { 5 } { 12 } {/tex} and {tex} \frac { x } { 2 } + y = 1 {/tex} is

A

{tex} 1 / 2 {/tex}

{tex} 3 / 2 {/tex}

C

{tex}2{/tex}

D

{tex} 5 / 2 {/tex}

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Q 6. If {tex} 1 - \frac { 1 } { x } = \frac { x + 1 } { x } , {/tex} what does {tex} x {/tex} equal to {tex} ? {/tex}

A

{tex}1{/tex} or {tex}2{/tex}

B

{tex} + 1 {/tex}

C

{tex} +1\ and -1 {/tex}

{tex} 0 {/tex}

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Q 7. {tex} \mathrm{Assertion} {/tex}: The graph of equation y + 8 = x + 8 passes through origin. {tex} \mathrm{Reason} {/tex}: The graph of a linear equation with its constant term = 0 always passes through origin.

Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'

B

Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'

C

Assertion is true but Reason is false

D

Assertion is false but Reason is true

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Q 8. {tex}\mathrm{Assertion}:{/tex}The equation {tex} 2 x + 3 y = 3 ( 2 + y ) {/tex} has a unique solution.
{tex}\mathrm{Reason}:{/tex} The linear equation in two variables has a unique solution.

A

Both Assertion and Reason are true and Reason is the correct explanation of 'Assertion'

B

Both Assertion and Reason are true and Reason is not the correct explanation of 'Assertion'

Assertion is true but Reason is false

D

Assertion is false but Reason is true

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Q 9. What can be said regarding a line of its slope is zero

A

The line is {tex} x {/tex} -axis

The line is parallel to {tex} x {/tex} -axis

C

It passes through origin

D

none of these

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Q 10. If {tex} a{/tex} and {tex} b{/tex} are real no's the equation {tex} 3 x - 5 + a = b x + 1 {/tex} has a unique solution {tex} x {/tex}

A

For all {tex} a{/tex} and {tex} b{/tex}

B

if {tex} a \neq 2 b {/tex}

C

if {tex} a \neq b {/tex}

if {tex} b \neq 3 {/tex}

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Q 11. The equations {tex} 2 x + y - 5 = 0 {/tex} and {tex} 6 x + 3 y - 15 = 0 {/tex} shows

A

Coincident lines

B

Infinite number of solution

C

Unique solution

Both (A) and (B)

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Q 12. If {tex} \mathrm { p } > \mathrm { q } {/tex} and {tex} \mathrm { r } < 0 , {/tex} which of the following is/are true:-

A

{tex} \mathrm { pr } < \mathrm { qr } {/tex}

B

{tex} \mathrm {p + r > q + r} {/tex}

C

{tex} \mathrm{p - r < q - r} {/tex}

Both (A) and (B)

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Q 13. The pair of equations {tex} y = 0 {/tex} and {tex} y = - 7 {/tex} has :

A

one solution

B

two solutions

C

infinitely many solutions

no solution

##### Explanation

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Q 14. One equation of a pair of dependent linear equations is {tex} - 5 x + 7 y = 2 . {/tex} The second equation can be :

A

{tex} 10 x + 14 y + 4 = 0 {/tex}

B

{tex} - 10 x - 14 y + 4 = 0 {/tex}

C

{tex} - 10 x + 14 y + 4 = 0 {/tex}

{tex} 10 x - 14 y = - 4 {/tex}

##### Explanation

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Q 15. A pair of linear equations which has a unique solution {tex} x = 2 , y = - 3 {/tex} is :

A

{tex} x + y = - 1 {/tex}
{tex} 2 x - 3 y = - 5 {/tex}

B

{tex} 2 x + 5 y = - 11 {/tex}
{tex} 4 x + 10 y = - 22 {/tex}

C

{tex} x - 4 y - 14 = 0 {/tex}
{tex} 5 x - y - 13 = 0 {/tex}

Both B and C

##### Explanation

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Q 16. 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:

A

4 and 24

B

5 and 30

6 and 36

D

3 and 24

##### Explanation

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Q 17. Sum of the digits of a 2-digit number is 9. When the digits are reversed (interchanged), it is found that the resulting number is greater than the original number by 27. Find the number.

A

63

B

45

C

54

36