Question

Draw the graph of the pair of equations 2x + y = 4 & 2x - y =8. Write the vertices of a triangle formed by these lines and the y-axis , also find the area of the triangle.

wrong answers would be reported, please don't waste my time by answering wrong. Don't answer if you don't know it.

Answer 1

Answer:

A1/a2=b1/b2=c1/c2. 2x/2x=1/1. y/y=1/1. -4/-8=1/2 they are parallel lines

Answer 2

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

Given pair of lines are

$\rm :\longmapsto\:2x + y = 4$

and

$\rm :\longmapsto\:2x - y = 8$

Consider,

$\rm :\longmapsto\:2x + y = 4$

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

$\rm :\longmapsto\:2 \times 0 + y = 4$

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

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

$\rm :\longmapsto\:2x + 0 = 4$

$\rm :\longmapsto\:2x = 4$

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

Hᴇɴᴄᴇ,

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

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

➢ Now draw a graph using the points (0 , 4) & (2 , 0)

➢ See the attachment graph.

Consider,

$\rm :\longmapsto\:2x - y = 8$

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

$\rm :\longmapsto\:2 \times 0 - y = 8$

$\rm :\longmapsto\: - y = 8$

$\rm :\longmapsto\: y = - \: 8$

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

$\rm :\longmapsto\:2x - 0 = 8$

$\rm :\longmapsto\:2x = 8$

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

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 8 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 8) & (4 , 0)

➢ See the attachment graph.

Thus,

From graph, we concluded that triangle ABC is the required area bounded between the given lines with y - axis having vertices as

Coordinates of A = ( 3, - 2 )

Coordinates of B = ( 0, 4 )

Coordinates of C = ( 0, - 8 )

So,

Area of triangle ABC = 1/2 × 12 × 3 = 18 square units.