Question

Find the value of α for which the following pair of equations has infinite number of

solutions: αx + 3y = α – 3

12x + αy = α​

Answer 1

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From Determinant...

JEE CONCEPT

For infinte solutions

a1/a2 =b1/b2 = c1/c2

Answer 2

$\alpha$x + 3y = $\alpha$ - 3

12x + $\alpha$y = $\alpha$

_________ [ GIVEN ]

• We have to find the value of $\alpha$ if they have infinite number of solutions.

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Infinite number of solutions :

$\dfrac{ a_{1}}{ a_{2} }$ = $\dfrac{ b_{1}}{ b_{2} }$ = $\dfrac{ c_{1}}{ c_{2} }$

Here ..

• $a_{1}$ = $\alpha$

• $a_{2}$ = 12

• $b_{1}$ = 3

• $b_{2}$ = $\alpha$

• $c_{1}$ = $\alpha$ - 4

• $c_{2}$ = $\alpha$

=> $\dfrac{\alpha}{12}$ = $\dfrac{\alpha}{3}$

Cross-multiply them

=> ${ \alpha }^{2}$ = 12 × 3

=> ${ \alpha }^{2}$ = 36

=> $\alpha$ = √36

=> $\alpha$ = 6

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$\alpha$ = 6

_______ [ ANSWER ]

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