Question

Solve by graphical method x-y =-2
4x-y=4​

Answer 1

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

Given pair of linear equations are

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

and

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

Now, Consider

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

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

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

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

$\bf\implies \:y = 2$

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

$\rm :\longmapsto\:x - 0 = - 2$

$\bf\implies \:x = - 2$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2 \\ \\ \sf - 2 & \sf 0 \end{array}} \\ \end{gathered}$

Now, Consider

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

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

$\rm :\longmapsto\:4 \times 0 - y = 4$

$\rm :\longmapsto\:0 - y = 4$

$\rm :\longmapsto\: - y = 4$

$\bf\implies \:y = - 4$

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

$\rm :\longmapsto\:4x - 0 = 4$

$\rm :\longmapsto\:4x = 4$

$\bf\implies \:x = 1$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4 \\ \\ \sf 1 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

From graph we concluded that system of equations is consistent having unique solution and solution is

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 4} \end{cases}\end{gathered}\end{gathered}$