What will be shown in the graph of the equations (15x+10y=40) and (3x+2y=8)?
Answer and explanation
Correct answer: Same line
Every coefficient and the constant in the first equation is 5 times the corresponding term in the second: \(15x+10y=40=5(3x+2y=8)\). Hence, both equations have the same solution set, so their graphs coincide as the same line. Option B is incorrect because distinct parallel lines require the coefficients to be proportional but the constants not to be proportional. Exam tip: when one complete linear equation is a non-zero multiple of the other, the lines are coincident and the pair has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
Same line
Why is this the correct answer?
Every coefficient and the constant in the first equation is 5 times the corresponding term in the second: \(15x+10y=40=5(3x+2y=8)\). Hence, both equations have the same solution set, so their graphs coincide as the same line. Option B is incorrect because distinct parallel lines require the coefficients to be proportional but the constants not to be proportional. Exam tip: when one complete linear equation is a non-zero multiple of the other, the lines are coincident and the pair has infinitely many solutions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
