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.
For which value of \(k\), linear pair \(x+y-4=0,2x+ky-3=0\) has no solution?
2
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).
In a two digit number, the unit digit is \(x\) and the tens digit is \(y\), then that number is
[PYQ 2025]
Options are free to see. Unlock the correct answer and full explanation with Pass.
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]
Options are free to see. Unlock the correct answer and full explanation with Pass.
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
Options are free to see. Unlock the correct answer and full explanation with Pass.
The pair satisfying \(3x+2y=11\) is -
[PYQ 2023]
Options are free to see. Unlock the correct answer and full explanation with Pass.
Write the condition for unique solutions of pair of equation \({a}_{1}x+{b}_{1}y+{c}_{1}=0\) and \({a}_{2}x+{b}_{2}y+{c}_{2}=0\).
Options are free to see. Unlock the correct answer and full explanation with Pass.
The pair satisfying 3x+2y=11 is:
Options are free to see. Unlock the correct answer and full explanation with Pass.
Practice more Board Maths PYQs
Browse every Maths chapter, or explore the full Board question bank.
➗ All Maths chapters →