Find m for infinitely many solutions of 7x + (m − 4)y = 13 and 14x + 6y = 26.
Answer and explanation
Correct answer: m = 7
For two linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to have infinitely many solutions, the corresponding coefficients and constants must be proportional: a1/a2 = b1/b2 = c1/c2. Here, 7/14 = 13/26 = 1/2. Therefore, (m − 4)/6 must also equal 1/2. Solving gives 2(m − 4) = 6, so m − 4 = 3 and m = 7. Thus option B is correct. The other values do not make all three ratios equal; they would represent either intersecting or parallel distinct lines, not the same line.
Frequently asked questions
What is the correct answer to this question?
m = 7
Why is this the correct answer?
For two linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to have infinitely many solutions, the corresponding coefficients and constants must be proportional: a1/a2 = b1/b2 = c1/c2. Here, 7/14 = 13/26 = 1/2. Therefore, (m − 4)/6 must also equal 1/2. Solving gives 2(m − 4) = 6, so m − 4 = 3 and m = 7. Thus option B is correct. The other values do not make all three ratios equal; they would represent either intersecting or parallel distinct lines, not the same line.
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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