if-the-x-a-y-b-1-passes-through-the-point-lf-intersection-of-the-lines-x-y-3-and-2x-3y-1-and-is-parallel-to-the-line-y-x-6-then-find-the-value-of-a-and-b-

Question Number 29276 by gyugfeet last updated on 06/Feb/18

i f t h e \frac{x}{a} + \frac{y}{b} = 1 p a s s e s t h r o u g h t h e p o i n t l f i n t e r s e c t i o n o f t h e l i n e s x + y = 3 a n d 2 x - 3 y = 1 a n d i s p a r a l l e l t o t h e l i n e y = x - 6 t h e n f i n d t h e v a l u e o f a a n d b .

Answered by Rasheed.Sindhi last updated on 06/Feb/18

Intersection point of x + y = 3 a n d 2 x - 3 y = 1

y = 3 - x \Rightarrow 2 x - 3 (3 - x) = 1

x = 2, y = 1

\cap tersection point (2, 1)

The line \frac{x}{a} + \frac{y}{b} = 1 passes through (2, 1)

∴ \frac{2}{a} + \frac{1}{b} = 1 \dots \dots \dots \dots \dots \dots \dots . (A)

This line is parallel to y = x - 6, so they

have same slope

\frac{x}{a} + \frac{y}{b} = 1 \Rightarrow b x + a y = a b

y = - \frac{b}{a} x + b

- \frac{b}{a} = 1

a = - b

(A) \Rightarrow \frac{2}{- b} + \frac{1}{b} = 1 \Rightarrow b = - 1, a = - (- 1) = 1

a = 1, b = - 1