Question

Solve graphically , 3x + y -12 = 0 and x – 3y + 6 = 0. Shade the region bounded by the lines and x- axis.Also, find the area of shaded region.
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Answer 1

Answer:

So we have, 2x+3y=4 and x-y+3=0

Now 2x+3y=4

= x= 4−3y2

When y=0 then, x=2

When y=2 then, x=-1

Thus, we have the following table giving points on the line x+y=4

X -1 2

Y 2 0

Now ,    x-y+3=0

=x=y-3

When y=3, then x=0

When y=4, then x= 1

Thus, we have the following table giving points on the line x-y+3=0

X 0 1

Y 3 4

Graph of the equation 2x+3y=4 and x-y+3=0

8

Clearly two lines intersect at (-1, 2)

Hence x=-1 and y=2 is the solution of the given system of equations.