Choose the correct statement about 3x − y = 4 and 6x − 2y = 9.
Answer and explanation
Correct answer: It has no solution
Write the equations in the standard form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. Their coefficient ratios are a1/a2 = 3/6 = 1/2 and b1/b2 = (−1)/(−2) = 1/2, but the constant ratio is c1/c2 = (−4)/(−9) = 4/9, which is not 1/2. Thus the coefficients are proportional while the constants are not. Geometrically, the two lines have the same slope but different intercepts, so they are distinct parallel lines. Distinct parallel lines never meet; therefore the pair has no solution, making option C correct.
Frequently asked questions
What is the correct answer to this question?
It has no solution
Why is this the correct answer?
Write the equations in the standard form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. Their coefficient ratios are a1/a2 = 3/6 = 1/2 and b1/b2 = (−1)/(−2) = 1/2, but the constant ratio is c1/c2 = (−4)/(−9) = 4/9, which is not 1/2. Thus the coefficients are proportional while the constants are not. Geometrically, the two lines have the same slope but different intercepts, so they are distinct parallel lines. Distinct parallel lines never meet; therefore the pair has no solution, making option C correct.
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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