Question

Find the nature of solution of the pair of linear equation x - 2y = 5 and 2x - 4y = 1.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations is

$\rm :\longmapsto\:x - 2y = 5 - - - (1)$

and

$\rm :\longmapsto\:2x - 4y = 1 - - - (2)$

Consider, Line (1)

$\rm :\longmapsto\:x - 2y = 5$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - 2y = 5$

$\rm :\longmapsto\: - 2y = 5$

$\rm :\longmapsto\: y = - 2.5$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 2(0) = 5$

$\rm :\longmapsto\:x = 5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 2.5 \\ \\ \sf 5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 2.5) & (5 , 0)

➢ See the attachment graph.

Consider, Line (2)

$\rm :\longmapsto\:2x - 4y = 1$

Substituting 'y = 1' in the given equation, we get

$\rm :\longmapsto\:2x - 4 = 1$

$\rm :\longmapsto\:2x = 1 + 4$

$\rm :\longmapsto\:2x = 5$

$\rm :\longmapsto\:x = 2.5$

Substituting 'y = 2' in the given equation, we get

$\rm :\longmapsto\:2x - 4(2)= 1$

$\rm :\longmapsto\:2x - 8= 1$

$\rm :\longmapsto\:2x = 1 + 8$

$\rm :\longmapsto\:2x = 9$

$\rm :\longmapsto\:x = 4.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2.5 & \sf 1 \\ \\ \sf 4.5 & \sf 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (2.5 , 1) & (4.5 , 2)

➢ See the attachment graph.

From graph,

We concluded that system of linear equation is inconsistent having no solution.