Question

Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.

Answer 1

x + 2y = 4
⇒ x = 4 - 2y
The table of x + 2y = 4 is

X	2	- 4	12
Y	1	4	- 4

3x - 2y = 4
⇒ x = `(4 + 2y)/(3)`
The table of 3x - 2y = 4 is

X	2	4	6
Y	1	4	7

Now plotting the points on a graph and we get the following required graph:

Therefore the solution of the given system of equations is (2,1).
Thus the vertices of the triangle are:
A(2,1), B`(4/3,0)`and C(4,0)
AB ⊥ BC and D ≡ (2,0)
AD = 1 and BC = `2(2)/(3) "units" = (8)/(3) "units"`
Area of the triangle ABC = `(1)/(2) xx "AD" xx "BC"`

= `(1)/(2) xx 1 xx (8)/(3)`

= `(4)/(3)"sq.units"`

= `1(1)/(3)"sq.units"`