Gujarati
Hindi
3 and 4 .Determinants and Matrices
normal

Number of triplets of $a, b \, \& \,c$ for which the system of equations,$ax - by = 2a - b$ and $(c + 1) x + cy = 10 - a + 3 b$ has infinitely many solutions and $x = 1, y = 3$ is one of the solutions, is :

A

exactly one

B

exactly two

C

exactly three

D

infinitely many

Solution

put $x = 1\,  $ and $\, y = 3$ in $1^{st}$ equation ==> $a$ = $- 2b$ and from $2^{nd}$ equation

$c =$ $ \frac{{9\,\, + \,\,5\,b}}{4}$ ;

Now use $\frac{a}{{c\,\, + \,\,1}}$ $=$ $-\frac{b}{c}$ $=$ $\frac{{2\,a\,\, – \,\,b}}{{10\,\, – \,\,a\,\, + \,\,3\,b}}$ ;

from first two $b = 0$ or $c = 1$ ;

if $b = 0 ==> a = 0\, $ and $ \, c = 9/4$ ;

if $c = 1 ; b = – 1 ; a = 2$

Standard 12
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.