Question

if (a,-2a) is a point on line 2x-3y=-1 ,then find the value of a.​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

CONCEPT TO BE IMPLEMENTED

If a point lies on a straight line then the point satisfies the equation of the line

GIVEN

$\sf{ \: (a,-2a) \: is \: a \: point \: on \: line \: 2x-3y=-1}$

TO DETERMINE

The value of a

CALCULATION

The given equation of the line is

$\sf{ \: 2x-3y=-1} \: \: \: ....(1)$

Now

$\sf{ \: (a,-2a) \: is \: a \: point \: on \: line \: 2x-3y=-1}$

So the point satisfies the equation of the line

$\therefore \: \sf{ 2a-3 \times ( - 2a)=-1}$

$\implies \: \: \sf{ 2a + 6a=-1}$

$\implies \: \: \sf{ 8a=-1}$

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

RESULT

The required answer is

$\boxed{ \displaystyle \:\: \: \sf{a = - \frac{1}{8} } \: \: \: }$

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