Question

Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x+y=6
4x-2 y=4

Answer 1

2x+y=6
4x-2 y=4
\begin{tabular}{|l|l|l|l|} \hline\( x \) & 0 & 1 & 2 \\ \hline\( y \) & 6 & 4 & 2 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline\( x \) & 0 & 1 & 2 \\ \hline\( y \) & \( -2 \) & 0 & 2 \\ \hline \end{tabular}
Here, $a_1=2,b_2=1,c_1=6$
$$a_1=4,b_2=-2,c_1=4$$
$$\therefore \frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2},\frac{b_1}{b_2}=-\frac{1}{2},\frac{c_1}{c_2}=\frac{6}{4}=\frac{3}{2}$$
$$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\ne \frac{c_1}{c_2}$$
$\therefore$ two lines are consistent