Question

Draw the graph of 2x + y - 6 = 0 and 2x - y = -2. Also, find the area of the triangle formed by
the above lines and X-axis.​

Answer 1

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

The given equation of lines are

$\rm :\longmapsto\:2x + y - 6 = 0 - - - (1)$

and

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

Consider, Line (1),

$\rm :\longmapsto\:2x + y - 6 = 0$

$\rm :\longmapsto\:2x + y = 6$

On substituting x = 0, we get

$\rm :\longmapsto\:2(0) + y = 6$

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

On substituting y = 0, we get

$\rm :\longmapsto\:2x + 0 = 6$

$\rm :\longmapsto\:2x = 6$

$\rm :\longmapsto\:x = 3$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Consider, Line (2)

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

On substituting x = 0, we get

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

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

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

On substituting y = 0, we get

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

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

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

Hᴇɴᴄᴇ,

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

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

➢ Now draw a graph using the points.

➢ See the attachment graph.

From graph we concluded that the triangle formed by these lines with x - axis is ABC.

Given coordinates are

• Coordinates of A be (- 1, 0)

• Coordinates of B (3, 0)

• Coordinates of C (1, 4)

[ Please see the attachment ].

Thus,

Area of triangle ABC = 1/2 × BASE × HEIGHT

Area of triangle = 1/2 × 4 × 4 = 8 sq. units.

Answer 2

Answer:

it's ok. abhi joh kiya hai uske liye maf karti hu. mare points waste ho gaye