# Class 9

Explore popular questions from Linear Equations in 2 Variables for Class 9. This collection covers Linear Equations in 2 Variables previous year Class 9 questions hand picked by experienced teachers.

# Mathematics

Linear Equations in 2 Variables

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Q 1. Every linear equation in {tex} x {/tex} and {tex} y {/tex} represents a

A

straight line passing through origin

B

straight line parallel to {tex} y {/tex} axis

C

straight line parallel to {tex} x {/tex} axis

straight line

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Q 2. Every linear equation in two variables has

Infinite number of solutions

B

Unique solutions

C

No solution

D

Two solutions

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Q 3. To verify the ordered pair {tex} ( \alpha , \beta ) {/tex} be the solution to linear equation {tex} a x + b y + c = 0 {/tex}

A

Substitute {tex} \mathrm{( \alpha , \beta )} {/tex} in place of {tex} \mathrm x {/tex} and {tex}\mathrm y {/tex} and {tex}\mathrm { L. H.S.} {/tex} should be positive

B

{tex} \mathrm {a \alpha + b y + c }{/tex} must be zero

{tex} \mathrm { a } \alpha + \mathrm { b } \beta + \mathrm { c } {/tex} must be zero

D

Find the value of {tex} \mathrm{a \alpha + b \beta + c} {/tex} which must be zero

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Q 4. One side of a right angled triangle is 20 inches and the hypotenuse is 10 inches longer than the other side. The hypotenuse is (in inches)

A

15

25

C

12

D

20

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Q 5. For what value of a, the equations {tex} x - y = a {/tex} has {tex} x = 1 {/tex} and {tex} y = 1 {/tex} as a solution.

A

any real number

B

any positive real number

{tex} 0 {/tex}

D

{tex} 1 {/tex}

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Q 6. The coordinates of the point where the equation {tex} 2 x + y = 6 {/tex} cuts the {tex} x {/tex} axis

A

{tex} ( 0,3 ) {/tex}

{tex} ( 3,0 ) {/tex}

C

{tex} ( 2,0 ) {/tex}

D

{tex} ( 0,2 ) {/tex}

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Q 7. For what value of {tex} \mathrm { k } , {/tex} the given equations have unique solution
{tex} \mathrm { kx } + 2 \mathrm { y } = 5 ; 3 \mathrm { x } + \mathrm { y } = 1 {/tex}

{tex} \mathrm k \neq 6 {/tex}

B

{tex} \mathrm k = 6 {/tex}

C

{tex} \mathrm { k } = - 6 {/tex}

D

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

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Q 8. The ratio of the price of coffee to that of tea is {tex} 8: 1 . {/tex} If the price of coffee is {tex} 200 \mathrm { Rs } / 100 \mathrm { gm } . {/tex} Find the cost of {tex} 100 \mathrm { gm } {/tex} of tea.

A

{tex} \mathrm { Rs } .1600 {/tex}

B

{tex} \mathrm { Rs } .192 {/tex}

C

{tex} \mathrm { Rs } .78 {/tex}

{tex} \mathrm { Rs }. 25 {/tex}

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Q 9. Assertion: The graph of equation {tex} y + 1 = x + 1 {/tex} passes through origin
Reason: The graph of a linear equation with its constant term {tex} \geq 0 {/tex} always passes through origin.

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 10. Assertion: The linear equation in two variables has a unique solution.
Reason: Every point on the graph of a linear equation in two variables is a solution of the linear equation.

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'

C

Assertion is true but Reason is false

Assertion is false but Reason is true

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Q 11. Match the following:

Column I Column II
(A) {tex}x = 2{/tex} (P) (B) {tex}y+2 = 0{/tex} (Q) (C) {tex}2y - 4 = 0{/tex} (R) (D) {tex}8x + 16 = 0{/tex} (S) A

{tex} ( \mathrm { A } ) - ( \mathrm { S } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { R } ) {/tex}

{tex} ( \mathrm D ) - ( \mathrm Q ) {/tex}

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Q 12. A man spends one fourth of his salary on house rent, one third on food and one -sixth on travel. After spending one-tenth of the remaining amount, he is left with Rs. 1350 . What is the difference between the amounts spent on house rent and food?

A

Rs. 750

B

Rs. 1000

C

Rs. 400

Rs. 500

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Q 13. {tex} \mathrm { x } + \mathrm { y } = 0 ; 2 \mathrm { x } + 2 \mathrm { y } = 0 \mathrm \ {/tex} has

A

no solution

B

one solution

C

two solution

more than two solutions

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Q 14. The points {tex} ( 7,2 ) {/tex} and {tex} ( - 1,0 ) {/tex} lie on a line

A

{tex} 7 y = 3 x - 7 {/tex}

{tex} 4 y = x + 1 {/tex}

C

{tex} y = 7 x + 7 {/tex}

D

{tex} x = 4 y + 1 {/tex}

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Q 15. The total no of integral pairs {tex} ( \mathrm { x } , \mathrm { y } ) {/tex} satisfying the equation {tex} \mathrm { x } + \mathrm { y } = \mathrm { xy } {/tex} is

A

0

B

1

2

D

none of these

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Q 16. The equations {tex} 2 \mathrm { x } + \mathrm { y } - 5 = 0 {/tex} and {tex} 6 \mathrm { x } + 3 \mathrm { y } - 15 = 0 {/tex} shows

A

coincident lines

B

infinite solutions

Both A and B

D

no solution

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Q 17. The solution of the given equation is {tex} 3 x - 2 y = 4 {/tex} is

A

{tex} ( 0 , - 2 ) {/tex}

B

{tex} ( - 2 , - 5 ) {/tex}

C

{tex} ( 2,1 ) {/tex}

All of the above

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Q 18. The given system of linear equations is inconsistent then

A

the lines are intersecting

B

the lines are parallel

C

the system has no common point

Both B and C

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Q 19. Match the following:

Column I Column II
(A) {tex}2x + 3y = 11{/tex} (P) {tex}(0,0){/tex}
(B) {tex}3x + 7y = 16{/tex} (Q) {tex}(3,1){/tex}
(C) {tex}x + y = 4{/tex} (R) {tex}(1,3){/tex}
(D) {tex}x - y = 0{/tex} (S) {tex}(4,1){/tex}

A

{tex} ( \mathrm { A } ) - ( \mathrm { P } ) {/tex}

{tex} ( \mathrm { B } ) - ( \mathrm { Q } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}

D

{tex} ( \mathrm { D } ) - ( \mathrm { R } ) {/tex}