Check whether the pair of equations $x - 2 y = 2, 4 x - 2 y = 5$ is consistent. [ 2 MARKS]

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Solution

Concept : 1 Mark
Calculation : 1 Mark

Given equations are,

$x - 2 y = 2, \Rightarrow x - 2 y - 2 = 0 \dots \dots (i)$

$a_{1} = 1, b_{1} = - 2, c_{1} = - 2$

$4 x - 2 y = 5 \Rightarrow 4 x - 2 y - 5 = 0 \dots \dots (i i)$

$a_{2} = 4, b_{2} = - 2, c_{2} = - 5$

For pair of equations to be consistent,

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ OR $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Here,

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Since , $\frac{1}{4} \neq \frac{- 2}{- 2} \Rightarrow \frac{1}{4} \neq - 1$

$\Rightarrow$ Pair of equations have unique solution

$∴$ pair of equations is consistent.

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Determine, graphically whether the system of equations x - 2y = 2, 4x - 2y = 5 is consistent or in-consistent.

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