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Find the value of F for which each of the following system of equations having infinitely many solution: 2a+3y=2, (F+2)a+(2F+1)y=2(F-1)
CBSE | Class 10 | Exercise 3.5 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
Find the value of F for which each of the following system of equations having infinitely many solution: 2a+3y=2, (F+2)a+(2F+1)y=2(F-1)

Given system of equations is:

2a+3y-2=0

(F+2)a+(2F+1)y-2(F-1)=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}}=2,{{b}_{1}}=3,{{c}_{1}}=-5

{{a}_{2}}=\left( F+2 \right),{{b}_{2}}=\left( 2F+1 \right),{{c}_{2}}=-2\left( F-1 \right)

So according to the question,

For unique solution, the condition is

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

2/\left( F+2 \right)=3/\left( 2F+1 \right)=-2/-2\left( F-1 \right)

2/\left( F+2 \right)=3/\left( 2F+1 \right)And 3/\left( 2F+1 \right)=2/2\left( F-1 \right)

\Rightarrow 2\left( 2F+1 \right)=3\left( F+2 \right)And 3\left( F-1 \right)=\left( 2F+1 \right)

\Rightarrow 4F+2=3F+6And 3F-3=2F+1

\Rightarrow F=4And F=4

Therefore, the given system of equations will have infinitely many solutions, if F=4.

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