Check whether the pair of equations x−2y=24x−2y=5is con

SOLUTION

Concept : 1 Mark
Calculation : 1 Mark

Given equations are,

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

$a_1=1,b_1=-2,c_1=-2$

$4x-2y=5\Rightarrow 4x-2y-5=0\dots \dots \left(ii\right)$

$a_2=4,b_2=-2,c_2=-5$

For pair of equations to be consistent,

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ OR $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here,

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

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

$\Rightarrow$ Pair of equations have unique solution

$\therefore$ pair of equations is consistent.