Question

Example 4). Check graphically whether the pair of equation x + 3y = 6 and 2x - 3y = 12 is consisten
t. If so, solve them graphically.​

Answer 1

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

Given pair of linear equations are

$\rm :\longmapsto\:x + 3y = 6 - - - (1)$

and

$\rm :\longmapsto\:2x - 3y = 12 - - - (2)$

Now, Consider Equation (1),

$\rm :\longmapsto\:x + 3y = 6$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2 \\ \\ \sf 6 & \sf 0 \end{array}} \\ \end{gathered}$

Now, Consider Equation (2),

$\rm :\longmapsto\:2x - 3y = 12 - - - (2)$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4 \\ \\ \sf 6 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

So, Solution of pair of linear equation is given by

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x = 6} \\ \\ &\sf{y = 0} \end{cases}\end{gathered}\end{gathered}$

Hence, pair of linear equations is consistent having unique solution