Question

draw the graphs of 2x+y=6 and 2x-y+2=0. shade the region bounded by these lines and x axis. find the area of shaded region

Answer 1

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Answer 2

SOLUTIONS:

We have,

2x + y = 6 _________(i)

2x - y + 2 = 0 _________(ii)

Graph of the equation 2x + y = 6:

We have,

2x + y = 6

y = 6 - 2x

When x = 0, we have y = 6

When x = 3, we have y = 0

Therefore, solutions :- (0, 6), (3, 0)

Plotting these points on graph ( refer to attachment 1 )

We have,

2x - y + 2 = 0

y = 2x + 2

When x = 0, we have y = 2

When x = -1, we have y = 0

Therefore, solutions :- (0, 2) , (-1, 0)

Plotting these points on graph ( refer to attachment 1 )

It is evident from the graph that the two lines intersect at point P(1, 4). The area enclosed by the lines and x-axis is shown in the attachment 1.

Thus, x = 1, y = 4 is the solution of the given system of equations. Draw PM perpendicular from P on x-axis.

Clearly, we have

PM = y-coordinate of point P(1, 4)

PM = 4

DB = 4

∴ Area of the shaded region = Area of ∆PBD

⇒ 1/2( DB × PM )

⇒ 1/2 × 4 × 4

⇒ 8 sq. units.