Find the value of F for which each of the following system of equations having infinitely many solution $4a+5y=3$, $ka+15y=9$

Home » Find the value of F for which each of the following system of equations having infinitely many solution ,

Find the value of F for which each of the following system of equations having infinitely many solution $4a+5y=3$ , $ka+15y=9$

Find the value of F for which each of the following system of equations having infinitely many solution $4a+5y=3$ , $ka+15y=9$

The Given equations are:

$4a+5y-3=0$

$ka+15y-9=0$

Above equations are of the form

${{a}_{1}}a+{{b}_{1}}y-{{c}_{1}}=0$

${{a}_{2}}a+{{b}_{2}}y-{{c}_{2}}=0$

Here, ${{a}_{1}}=4,{{b}_{1}}=5,{{c}_{1}}=-3$

${{a}_{2}}=F,{{b}_{2}}=15,{{c}_{2}}=-9$

According to the question,

For unique solution, the condition is

${{a}_{1}}/{{a}_{2}}={{b}_{1}}/{{b}_{2}}={{c}_{1}}/{{c}_{2}}$

$4/F=5/15=-3/-9$

$4/F=1/3$

$\Rightarrow F=12$

Therefore, given equations will have infinitely many solutions, if $F=12$ .

i

Sign up now and study all subjects for free