State true or false:
The following pair of linear equations is consistent.
$2 a x + b y = a$ and $4 a x + 2 b y - 2 a = 0; a, b \neq 0$

True

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False

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Solution

The correct option is A True
The given pair of linear equation can be written as
$2 a x + b y - a = 0$ and $4 a x + 2 b y - 2 a$
Here, $a_{1} = 2 a, b_{1} = b, c_{1} = - a$
And $a_{2} = 4 a, b_{2} = 2 b, c_{2} = - 2 a$
$∴ \frac{a_{1}}{a_{2}} = \frac{2 a}{4 a} = \frac{1}{2}$ and $\frac{b_{1}}{b_{2}} = \frac{b}{2 b} = \frac{1}{2}$ and $\frac{c_{1}}{c_{2}} = \frac{- a}{- 2 a} = \frac{1}{2}$
Here, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Thus, the given pair of linear equation is consistent.

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Similar questions

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

x + y = 0

3 x + 2 y = 5, 2 x - 3 y = 7

2 (a x - b y) + (a + 4 b) = 0

2 (b x + a y) + (b - 4 a) = 0

a_{1} x + b_{1} y + c_{1} = 0

a_{2} x + b_{2} y + c_{2} = 0

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

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