Find the value of F for which each of the following system of equations having infinitely many solution $Fa–2y+6=0$, $4a–3y+9=0$

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Find the value of F for which each of the following system of equations having infinitely many solution $Fa-2y+6=0$ , $4a-3y+9=0$

Find the value of F for which each of the following system of equations having infinitely many solution $Fa-2y+6=0$ , $4a-3y+9=0$

Given equations are:

$Fa-2y+6=0$

$4a-3y+9=0$

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, ${{a}_{1}}=F,{{b}_{2}}=-2,{{c}_{2}}=9$

${{a}_{2}}=4,{{b}_{2}}=-3,{{c}_{2}}=9$

According to the question,

For unique solution, the condition is

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

$F/4=-2/-3=2/3$

$F=8/3$

Therefore, given equations will have infinitely many solutions, if $F=8/3$ .

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