Question

aका वह मान ज्ञात कीजिए जिसके लिए निकाय ax+2y=2 8x+ay=4के अनन्त अनेक हल प्राप्त हो​

Answer 1

SOLUTION

TO DETERMINE

The value of a for which the equations have infinite number of solutions

ax + 2y = 2 , 8x + ay = 4

CONCEPT TO BE IMPLEMENTED

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions :

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}}$

Inconsistent :

No solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given equations are

ax + 2y = 2

8x + ay = 4

Now it is given that the equations have infinite number of solutions

Thus we get

$\displaystyle \sf{ \frac{ a}{8} = \frac{2}{a} = \frac{2}{4} }$

$\displaystyle \sf{ \implies \: \frac{ a}{8} = \frac{1}{2} }$

$\displaystyle \sf{ \implies \: a = \frac{8}{2} }$

$\displaystyle \sf{ \implies \: a = 4 }$

FINAL ANSWER

Hence the required value of a = 4

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Answer 2

Answer:

निकाय ax+2y=2 8x+ay=4के अनन्त अनेक हल प्राप्त हो