JIPMAT 2023 (QA) - <p>If the pair of linear equations 2x + 3y = 7 and 2px + (p + q) y = 28 has an infinite number of solutions, then (p, q):</p> | PYQs + Solutions

JIPMAT 2023

Algebra

Linear Equation

Conceptual

If the pair of linear equations $2x + 3y = 7$ and $2px + (p + q) y = 28$ has an infinite number of solutions, then $(p, q)$ :

(8,4)

(4,8)

(3,6)

(6,3)

Correct Option: 2

For infinite solutions, the equations must be proportional.

Given equations:

\newline

2x + 3y = 7

...(1)

\newline

2px + (p+q)y = 28

...(2)

For infinite solutions, coefficients must be proportional:

\frac{2}{2p} = \frac{3}{p+q} = \frac{7}{28}

From

\frac{7}{28} = \frac{1}{4}

\frac{2}{2p} = \frac{1}{4}

p = 4

And

\frac{3}{p+q} = \frac{1}{4}

\frac{3}{4+q} = \frac{1}{4}

3 = 4+q

q = 8

Therefore

(p,q) = (4,8)