Question

If 3x - 5y + 2 = Oand 9x + 3y + a = 0 represents the same straight line, find the value of a and b.
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Answer 1

SOLUTION

GIVEN

3x - by + 2 = Oand 9x + 3y + a = 0 represents the same straight line

TO DETERMINE

The value of a and b

EVALUATION

Here it is given that 3x - by + 2 = 0 and 9x + 3y + a = 0 represents the same straight line

So by the given condition

$\displaystyle \sf{ \frac{3}{9} = \frac{ - b}{3} = \frac{2}{a} }$

Now

$\displaystyle \sf{ \frac{3}{9} = \frac{ - b}{3} \: \: \: gives \: }$

$\displaystyle \sf{ \frac{1}{3} = \frac{ - b}{3} \: \: \: \: }$

$\displaystyle \sf{ \implies \: b = - 1 }$

Again

$\displaystyle \sf{ \frac{3}{9} = \frac{2}{a} \: \: \: gives}$

$\displaystyle \sf{ \frac{1}{3} = \frac{2}{a} \: \: \: }$

$\displaystyle \sf{ \implies \: a = 6}$

FINAL ANSWER

The required value a = 6 , b = - 1

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