Which statement is correct about the graph of (7x+9y=43) and (14x+18y=86)?
Answer and explanation
Correct answer: Same line
The first equation is 7x+9y=43. Multiplying every term by 2 gives 14x+18y=86, which is exactly the second equation. Multiplying an equation by a nonzero number does not change its set of solutions; it only writes the same relationship in a different form.
Therefore both equations represent one and the same straight line on the graph. Every point on that line satisfies both equations, so the pair has infinitely many solutions. Option B is correct. Distinct parallel lines would have proportional x- and y-coefficients but non-proportional constants; here the constant is also doubled.
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What is the correct answer to this question?
Same line
Why is this the correct answer?
The first equation is 7x+9y=43. Multiplying every term by 2 gives 14x+18y=86, which is exactly the second equation. Multiplying an equation by a nonzero number does not change its set of solutions; it only writes the same relationship in a different form.
Therefore both equations represent one and the same straight line on the graph. Every point on that line satisfies both equations, so the pair has infinitely many solutions. Option B is correct. Distinct parallel lines would have proportional x- and y-coefficients but non-proportional constants; here the constant is also doubled.
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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