Question

Draw and solve the equations Graphically : 2 x – y = 1 and x + 2y = 13​

Answer 1

Answer:

answer of your question

Answer 2

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

Given pair of linear equations are

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

and

$\rm :\longmapsto\:x + 2y = 13 - - - (2)$

Consider, Equation (1)

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

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

$\rm :\longmapsto\:2(0) - y = 1$

$\rm :\longmapsto\: - y = 1$

$\rm :\longmapsto\: y = - \: 1$

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

$\rm :\longmapsto\:2x - 0 = 1$

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

$\rm :\longmapsto\:x = 0.5$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 1 \\ \\ \sf 0.5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 1) & (0.5 , 0)

➢ See the attachment graph. [ Red Line ]

Consider, Equation (2),

$\rm :\longmapsto\:x + 2y = 13$

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

$\rm :\longmapsto\:0 + 2y = 13$

$\rm :\longmapsto\:2y = 13$

$\rm :\longmapsto\:y = 6.5$

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

$\rm :\longmapsto\:x + 2(0) = 13$

$\rm :\longmapsto\:x = 13$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6.5 \\ \\ \sf 13 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 6.5) & (13 , 0)

➢ See the attachment graph. [ Blue line ]

Hence,

From graph, we conclude that solution of given pair

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

and

$\rm :\longmapsto\:x + 2y = 13$

is

$\: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf \: (7,3)}}$