Question

If the system of equations 7x-y- 5=0 and ax-5y-25=0 has infinite number of solutions, then for k∈IR the general Solution (x,y) of the system is

Answer 1

Solution:

Two equations of line have infinite number of solutions if,

Ax +By =C

Px +Qy =R

$\frac{A}{P}=\frac{B}{Q}=\frac{C}{R}$

The two equation of line are

7 x-y= 5

ax-5 y=25

$\frac{7}{a}=\frac{-1}{-5}=\frac{5}{25}\\\\ a=35$

Let, y=k

7x-k=5

7 x = k+5

$x=\frac{k+5}{7}$

General solution of above two lines having infinite number of solutions

    $=(\frac{k+5}{7},k)$

where, k∈R