Question

draw the graph of the pair of linear equation x minus y + 2 is equal to zero and 4 x minus y minus 4 is equal to zero calculate the area of a triangle formed by the line so drawn and the x axis​

Answer 1

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

Given pair of line is

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

and

$\rm :\longmapsto\:4x - y - 4 = 0 - - - (2)$

Now, Consider Line (1),

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

can be rewritten as

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

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

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

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

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

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

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

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

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 draw a graph using the points (0 , 2) & (- 2 , 0)

➢ See the attachment graph.

Now, Consider Line (2),

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

can be rewritten as

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

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

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

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

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

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

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

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

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

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 (0 , - 4) & (1 , 0)

➢ See the attachment graph.

Hence, from graph we concluded that the required area bounded by the given lines with x - axis is ABC.

So, Required area of Triangle ABC

= area of triangle ADC - area of triangle ADB

$\rm \: = \:\dfrac{1}{2} \times 4 \times 4 - \dfrac{1}{2} \times 4 \times 1$

$\rm \: = \:8 - 2$

$\rm \: = \:6 \: square \: units$