Question

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

$2x-2y-2=0,4x-4y-5=0$.

Answer 1

Check pair of linear equations are consistent/inconsistent.

Given equations are:

$2x-2y-2=0,4x-4y-5=0$

Here,

$$\begin{gathered} a_1=2,b_1=-2,c_1=-2 \\ {a}_2=4,b_1=-4,c_1=-5 \end{gathered}$$

Now,

$$\begin{gathered} \frac{a_1}{a_2}=\frac{2}{4} \\ =\frac{1}{2} \\ \frac{b_1}{b_2}=\frac{-2}{-4} \\ =\frac{1}{2} \\ \frac{c_1}{c_2}=\frac{2}{5} \\ \therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2} \end{gathered}$$

Thus, these linear equations are parallel and have no possible solutions.

Hence, the pair of linear equations are inconsistent.