Online Test — Pair of Linear Equations in Two Variables
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
What type of solution do intersecting lines represent?
No solution
Unique solution
Infinite solutions
Two solutions
Explanation: Intersecting lines meet at exactly one point → unique solution
Question 2 of 10
medium
Solve by observation: x + y = 8, x − y = 2
x=5,y=3
x=3,y=5
x=6,y=2
x=4,y=4
Explanation: Adding gives 2x=10→x=5, then y=3
Question 3 of 10
medium
The pair 2x+3y=8 and 4x+6y=15 has:
Unique solution
No solution
Infinite solutions
Two solutions
Explanation: \(a_{1}\)/\(a_{2}\)=1/2, \(b_{1}\)/\(b_{2}\)=1/2, but \(c_{1}\)/\(c_{2}\)=8/15≠1/2 → parallel
Question 4 of 10
medium
Which method is best for: 3x+4y=10 and 3x−2y=4?
Substitution
Elimination by subtracting
Cross-multiplication
Graphing
Explanation: Both equations have the same $3x$ term, so subtracting one from the other eliminates $x$ at once: $6y = 6 \Rightarrow y = 1$, then $x = 2$. Elimination by subtraction is quickest here.
Question 5 of 10
medium
The sum of two numbers is 35 and their difference is 7. The numbers are:
20,15
21,14
22,13
19,16
Explanation: x+y=35, x−y=7 → 2x=42→x=21, y=14
Question 6 of 10
medium
For cross-multiplication, the denominator \(a_{1}b_{2}-a_{2}b_{1}\) = 0 means:
Unique solution
No solution
Either parallel or coincident
Always coincident
Explanation: Denominator zero means lines are either parallel or coincident
Question 7 of 10
medium
2 pens and 3 pencils cost ₹46. 4 pens and 2 pencils cost ₹68. Cost of 1 pen:
₹10
₹12
₹14
₹16
Explanation: Solve: 2p+3c=46, 4p+2c=68 → multiply first by2:4p+6c=92, subtract:4c=24→c=6, then p=14
Question 8 of 10
medium
Lines \(a_{1}x+b_{1}y+c_{1}\)=0 and \(a_{2}x+b_{2}y+c_{2}\)=0 are coincident if:
\(a_{1}\)/\(a_{2}\) ≠ \(b_{1}\)/\(b_{2}\)
\(a_{1}\)/\(a_{2}\) = \(b_{1}\)/\(b_{2}\) ≠ \(c_{1}\)/\(c_{2}\)
\(a_{1}\)/\(a_{2}\) = \(b_{1}\)/\(b_{2}\) = \(c_{1}\)/\(c_{2}\)
\(a_{1}\)/\(a_{2}\) ≠ \(c_{1}\)/\(c_{2}\)
Explanation: Coincident lines have all three ratios equal
Question 9 of 10
medium
A number consists of two digits whose sum is 8. If 18 is added, digits reverse. The number is:
26
35
44
53
Explanation: Let tens=x, units=y; x+y=8, 10x+y+18=10y+x → 9x-9y=-18→x-y=-2; solving: x=3,y=5 → 35
Question 10 of 10
medium
The solution of 2x+3y=11 and 3x+2y=9 is:
x=1,y=3
x=2,y=2
x=3,y=1
x=4,y=1
Explanation: Multiply first by2:4x+6y=22, second by3:9x+6y=27, subtract:5x=5→x=1, then y=3