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Pair of Linear Equations in Two Variables

7 Board Maths previous year questions on Pair of Linear Equations in Two Variables — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.

Q1 FREE PREVIEW

For which value of \(k\), linear pair \(x+y-4=0,2x+ky-3=0\) has no solution?

a

0

b

2

c

6

d

8

✓ Correct answer: b)

2

Explanation

The condition for no solution is \(\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\neq \frac{{c}_{1}}{{c}_{2}}\)

Here, \({a}_{1}=1,{b}_{1}=1,{c}_{1}=-4\) and \({a}_{2}=2,{b}_{2}=k,{c}_{2}=-3\)

Applying the condition:
\(\frac{1}{2}=\frac{1}{k}\)

Cross-multiplying gives:
\(k=2\)

Check the second part:

\(\frac{1}{k}\neq \frac{-4}{-3}\)

For k=2, this is \(\frac{1}{2}\neq \frac{4}{3}\)

which is true.

Therefore, the correct answer is (B).

Q2

In a two digit number, the unit digit is \(x\) and the tens digit is \(y\), then that number is

[PYQ 2025]

a

\((10x+y)\)

b

\((10y+x)\)

c

\((x+y)\)

d

\(10xy\)

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Q3

If twice the first number \(x\) is \(5\) less than \(7\) times the second number \(y\), then which of the following equations is correct?

[PYQ 2024]

a

\(2x=7y+5\)

b

\(5x=7y+2\)

c

\(7x=2y-5\)

d

\(2x=7y-5\)

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Q4

When
\(\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\neq \frac{{c}_{1}}{{c}_{2}}\)
then the system of equation
\({a}_{1}x+{b}_{1}y+{c}_{1}=0\) and \({a}_{2}x+{b}_{2}y+{c}_{2}=0\)
has

a

Unique solution

b

Two solutions

c

No solution

d

Infinitely many solution

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Q5

The pair satisfying \(3x+2y=11\) is -

[PYQ 2023]

a

\((1,4)\)

b

\((2,3)\)

c

\((3,5)\)

d

\((1,3)\)

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Q6

Write the condition for unique solutions of pair of equation \({a}_{1}x+{b}_{1}y+{c}_{1}=0\) and \({a}_{2}x+{b}_{2}y+{c}_{2}=0\).

a

\(\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\)

b

\(\frac{{a}_{1}}{{a}_{2}}\neq \frac{{b}_{1}}{{b}_{2}}\)

c

\(\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\neq \frac{{c}_{1}}{{c}_{2}}\)

d

\(\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}\)

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Q7

The pair satisfying 3x+2y=11 is:

a

(1,4)

b

(2,3)

c

(3,5)

d

(1,3)

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