Question

3x- y=7 and x+4y=11 graphic method​

Answer 1

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

Given pair of equation of lines is

$\rm :\longmapsto\:3x - y = 7$

and

$\rm :\longmapsto\:x + 4y = 11$

Consider,

$\rm :\longmapsto\:3x - y = 7$

can be rewritten as

$\rm :\longmapsto\:y = 3x - 7$

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

$\rm :\longmapsto\:y = 3(0) - 7$

$\rm :\longmapsto\:y =0 - 7$

$\bf\implies \:y = - 7$

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

$\rm :\longmapsto\:y = 3(1) - 7$

$\rm :\longmapsto\:y = 3 - 7$

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

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

$\rm :\longmapsto\:y = 3(2) - 7$

$\rm :\longmapsto\:y =6 - 7$

$\bf\implies \:y = - 1$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 7 \\ \\ \sf 1 & \sf - 4\\ \\ \sf 2 & \sf - 1 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Now, Consider

$\rm :\longmapsto\:x + 4y = 11$

can be rewritten as

$\rm :\longmapsto\:x = 11 - 4y$

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

$\rm :\longmapsto\:x = 11 - 4(0)$

$\rm :\longmapsto\:x = 11 - 0$

$\bf\implies \:x = 11$

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

$\rm :\longmapsto\:x = 11 - 4(1)$

$\rm :\longmapsto\:x = 11 - 4$

$\bf\implies \:x = 7$

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

$\rm :\longmapsto\:x = 11 - 4(2)$

$\rm :\longmapsto\:x = 11 - 8$

$\bf\implies \:x = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 11 & \sf 0 \\ \\ \sf 7 & \sf 1 \\ \\ \sf 3 & \sf 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

So, graph we concluded that

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: Solution-\begin{cases} &\bf{x = 3} \\ \\ &\bf{y = 2} \end{cases}\end{gathered}\end{gathered}$