What graph will be formed by (x+2y=3) and (2x+4y=6)?
Answer and explanation
Correct answer: The same line
The second equation is exactly twice the first: multiplying \\(x+2y=3\\) by 2 gives \\(2x+4y=6\\). Hence, both equations represent the same line and have infinitely many common solutions. Exam tip: check \\(a_1/a_2=b_1/b_2=c_1/c_2\\); when all three ratios are equal, the lines are coincident. Therefore, the parallel-lines option is not correct here because the two equations do not represent distinct lines.
Frequently asked questions
What is the correct answer to this question?
The same line
Why is this the correct answer?
The second equation is exactly twice the first: multiplying \\(x+2y=3\\) by 2 gives \\(2x+4y=6\\). Hence, both equations represent the same line and have infinitely many common solutions. Exam tip: check \\(a_1/a_2=b_1/b_2=c_1/c_2\\); when all three ratios are equal, the lines are coincident. Therefore, the parallel-lines option is not correct here because the two equations do not represent distinct lines.
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.
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