Question

Find the value of a for which the following linear
equations have infinite solutions:
2x + 5y = a
6x + 3a y = 3a​

Answer 1

For the equations to have infinite solutions :-

It should be like this for the equation

a1x + b1y - c1 = 0

a2x + b2y - c2 = 0

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

So here it is like this,

$\frac{2}{6} = \frac{5}{3a} = \frac{ - 1a}{ - 3a}$

So to find the value of a we should cross multiply 5/3a with 2/6

$\frac{2}{6} = \frac{5}{3} \times \frac{1}{a} \\ \\ \frac{1}{3} \times \frac{3}{5} = \frac{1}{a} \\ \\ \frac{1}{5} = \frac{1}{a} \\ \\ a = 5$

So, the required value of a is 5.

You can further check it by putting the value of a on every place.

Hope it helps