Question 3 (iii)
Are the following pair of linear equations consistent? Justify your answer
2a + by = a and 4a + 2by -2a = 0; a, b $\neq$ 0

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Solution

2ax + by – a = 0
and 4ax + 2by – 2a = 0
$h e r e, a_{1} = 2 a, b_{1} = b, c_{1} = - a; a_{2} = 4 a, b_{2} = 2 b, c_{2} = - 2 a n o w, \frac{a_{1}}{a_{2}} = \frac{2 a}{4 a} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{1}{2} = \frac{- a}{- 2 a} = \frac{1}{2} \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{1}{2}$
Hence, the given pair of linear equations has infinitely many solutions.

Hence the pair of linear equations is consistent

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2 a x + b y = a

4 a x + 2 b y - 2 a = 0; a, b \neq 0

Question 3 (iv)
Are the following pair of linear equations consistent? Justify your answer
x + 3y = 11 and 2(2x + 6y) = 22

Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

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