What value of (k) gives infinitely many solutions for (2x+ky=4) and (6x+9y=12)?
Answer and explanation
Correct answer: (3)
A pair of linear equations has infinitely many solutions when both equations represent exactly the same line. In standard form, this happens when the ratios of corresponding coefficients and constants are equal:
m a_1/a_2=b_1/b_2=c_1/c_2
m. This means one equation is a constant multiple of the other, so every point on one line also lies on the other. The equations here are already arranged in comparable standard form.
For
m 2x+ky=4
m and
m 6x+9y=12
m, the ratio from the x-coefficients is
m 2/6=1/3
m, and the constant ratio is
m 4/12=1/3
m. Therefore the y-coefficient must satisfy
m k/9=1/3
m. Multiplying by 9 gives
m k=3
m. Indeed, multiplying the first equation by 3 produces the second, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
A pair of linear equations has infinitely many solutions when both equations represent exactly the same line. In standard form, this happens when the ratios of corresponding coefficients and constants are equal:
m a_1/a_2=b_1/b_2=c_1/c_2
m. This means one equation is a constant multiple of the other, so every point on one line also lies on the other. The equations here are already arranged in comparable standard form.
For
m 2x+ky=4
m and
m 6x+9y=12
m, the ratio from the x-coefficients is
m 2/6=1/3
m, and the constant ratio is
m 4/12=1/3
m. Therefore the y-coefficient must satisfy
m k/9=1/3
m. Multiplying by 9 gives
m k=3
m. Indeed, multiplying the first equation by 3 produces the second, so option C is 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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