solve graphically the following equations: 2x + y = 6 and -2y + 3x = 2 , find the area of the triangle formed by two lines.

Answer :

We form a table for different values of x and y for both equations , As  :
 

2x + y = 6		3x -  2 y= 2
x	y	x	y
0	6	0	-1
1	4	0.67	0
2	2	2	2
3	0	4	5
5	- 4	6	8

Now we represent these points on x  -  y plane , As  :

we know are  of triangle  = $\frac{1}{2} \times \mathrm{Height} \times \mathrm{Base}$

So,

Area of triangle ABC = $\frac{1}{2} \times 2 \times 7 = \mathbf{7}\mathbf{ }\mathbf{ }{\mathbf{unit}}^{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$

And

Area of triangle ADE = $\frac{1}{2} \times 2 \times 2.33 = \mathbf{2}\mathbf{.}\mathbf{33}\mathbf{ }\mathbf{ }{\mathbf{unit}}^{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$