Find the value of F for which each of the following system of equations having infinitely many solution: $8a+5y=9$, $Fa+10y=18$

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Find the value of F for which each of the following system of equations having infinitely many solution: $8a+5y=9$ , $Fa+10y=18$

Find the value of F for which each of the following system of equations having infinitely many solution: $8a+5y=9$ , $Fa+10y=18$

Given equations are:

$8a+5y-9=0$

$Fa+10y-18=0$

The above equations are of the form

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

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

Now, ${{a}_{1}}=8,{{b}_{1}}=5,{{c}_{1}}=-9$

${{a}_{2}}=F,{{b}_{2}}=10,{{c}_{2}}=-18$

So according to the question,

For unique solution, the condition is

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

$8/F=5/10=-9/-18=1/2$

$\Rightarrow F=16$

Therefore, the given system of equations will have infinitely many solutions, if $F=16$ .

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