Question

Draw rhe graphs of linear equations x - 2y = 1 and 2x + y = 7 on the same graph and find their common solution ​

Answer 1

Answer:

Given linear equation is x - 2y = 1. It can be written as y = x - 1/2

Table of values

$\begin{lgathered}\begin{tabular}{| c | c | c | c |}\cline{1-4} \bf{x} & \sf{1} & \sf{ - 1} & \sf{3} \\ \cline{1-4}\bf{y} & \sf{0} & \sf{ -1} & \sf{1}\\ \cline{1-4} \end{tabular}\end{lgathered}$

Take 1 cm =1 unit on both axes. Plot the points (1, 0), (-1,-1) and (3, 1).

Draw a line passing through any two points. The graph of the linear equation (i) is shown in the adjoining figure. Other linear equation is

2x + y = 7.

It can be written as

y = 7 - 2x ...ii)

$\begin{lgathered}\begin{tabular}{| c | c | c | c |}\cline{1-4} \bf{x} & \sf{1} & \sf{2} & \sf{3} \\ \cline{1-4}\bf{y} & \sf{5} & \sf{3} & \sf{1}\\ \cline{1-4} \end{tabular}\end{lgathered}$

Plot the points (1, 5), (2, 3) and (3,1) on the same graph paper.

Draw a line passing through any two points. The graph of the linear equation (i) is shown in the above figure. We observe that the lines intersect each other at the point (3, 1). Therefore, the common solution of the given linear equations is (3, 1) ie. x = 3 and y = 1.