For all values of 'c' the pair of linear equations x-2y=8 and 5x-10y=c have a unique solution. justify whether this statement is true or false?

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Solution

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$T h e s y s t e m o f e q u a t i o n s a_{1} x + b_{1} y = c_{1} a n d a_{2} x + b_{2} y = c_{2} h a s a u n i q u e s o l u t i o n i f : \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} F o r t h e e q u a t i o n s x - 2 y = 8 a n d 5 x - 10 y = c, a_{1} = 1, a_{2} = 5, b_{1} = - 2, b_{2} = - 10, c_{1} = 8 a n d c_{2} = c H e r e, \frac{a_{1}}{a_{2}} = \frac{1}{5} a n d \frac{b_{1}}{b_{2}} = \frac{- 2}{- 10} = \frac{1}{5} S o, \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} . T h u s, t h e g i v e n s y s t e m o f e q u a t i o n s d o e s n' t h a v e a u n i q u e s o l u t i o n i r r e s p e c t i v e o f t h e v a l u e o f c .$

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Question 5
For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution. Justify whether it is true or false.

x - 2 y = 8

5 x - 10 y = 10

a m = b l,

a x + b y = c

l x + m y = n

k

x - 2 y = 3, 3 x + k y = 1

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