Question

Draw the graphs of 3x + 2y = 6 and 2x + y = 4. Shade the region bounded by these lines and y-axis. Find the area of shaded region.

Answer 1

Given : 3x + 2y = 6 and 2x + y = 4.

To Find : area of the region bounded by these lines and y-axis

Solution:

3x  + 2y  = 6

2x + y  = 4

& y  axis

Lets find vertex of triangle  at  y axis  x = 0

=> ( 0 , 3)    & ( 0 , 4) are vertex of triangle on  y axis

x = 2  , y = 0    ( 2, 0)  is third Vertex)

Base of triangle = 4 - 3 = 1

Altitude  =   2

Area of triangle = (1/2)(1) (2)  = 1  sq  units

area of shaded region. = 1  sq  units

or Area

( 0 , 3)    & ( 0 , 4) , ( 2, 0)

Area = (1/2) | 0(4 - 0) + 0(0-3) + 2(3 - 4)|  = (1/2) | - 2|  = 2/2 = 1

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