Question

Draw the graphs of the lines x+2y= 6 and 2x-y= 4.shade the area formed by these two lines and the y-axis.

Also, find the area.​

Answer 1

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

Given pair of linear equations are

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

and

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

Consider, First equation

$\red{\rm :\longmapsto\:x + 2y = 6}$

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

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

Consider second equation

$\red{\rm :\longmapsto\:2x - y = 4}$

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

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

So, the triangle formed by the given lines with y - axis is ABC having

• Coordinates of A (0, 3)

• Coordinates of B (0, - 4)

• Coordinates of C (2.8, 1.6)

So, Required area of triangle ABC is

$\rm \:  =  \: \dfrac{1}{2} \times 7 \times 2.8$

$\rm \:  =  \: 7 \times 1.4$

$\rm \:  =  \: 9.8 \: square \: units$