Linear Equations in Two Variables

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

straight line passing through origin

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

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

Unique solutions

No solution

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}

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

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

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

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)

15

25

12

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.

any real number

any positive real number

{tex} 0 {/tex}

{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

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

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

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

{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}

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

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

{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.

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

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

{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.

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

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

Assertion is true but Reason is false

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.

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

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

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) |

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

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

{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?

Rs. 750

Rs. 1000

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

no solution

one solution

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

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

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

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

{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

0

1

2

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

coincident lines

infinite solutions

Both A and B

no solution

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

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

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

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

All of the above

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

the lines are intersecting

the lines are parallel

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} |

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

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

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

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

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