Algebra

Matrices & Determinants

Easy

core

For what value of k, the following system of equations has infinitely many solutions?

$x + 2y = 5, 3x + ky = 15$

-3

✅ Correct Option: 2

For a system of equations to have infinitely many solutions, both equations must represent the same line. This occurs when the ratios of corresponding coefficients are equal:

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Given equations:

$x + 2y = 5$

$3x + ky = 15$

Identifying coefficients:

For equation 1: $a_1 = 1$ , $b_1 = 2$ , $c_1 = 5$

For equation 2: $a_2 = 3$ , $b_2 = k$ , $c_2 = 15$

Setting up the ratio equation:

$\frac{1}{3} = \frac{2}{k} = \frac{5}{15}$

Simplifying the constant ratio:

$\frac{5}{15} = \frac{1}{3}$

The ratios $\frac{1}{3} = \frac{1}{3}$ match.

Finding $k$ using the coefficient ratio:

$\frac{1}{3} = \frac{2}{k}$

$k = 2 \times 3$

$k = 6$

Therefore, $k = 6$ .

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For what value of k, the following system of equations has infinitely many solutions? x+2y=5,3x+ky=15x + 2y = 5, 3x + ky = 15x+2y=5,3x+ky=15

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For what value of k, the following system of equations has infinitely many solutions?

$x + 2y = 5, 3x + ky = 15$