Solve the equations graphically. 2x+y=2 , 2y-x=4. Also find the area of a triangle formed by the two lines and the line y=0
Answers
Given : 2x+y=2 , 2y-x=4.
To Find : the area of a triangle formed by the two lines and the line y=0
Solution:
2x+y=2
2y-x=4
y = 0
2x+y=2 , y = 0
=> point of intersection ( 1 , 0)
2y-x=4 , y = 0
=> point of intersection ( -4 , 0)
2x+y=2 , 2y-x=4
=> point of intersection ( 0 , 2)
Triangle is formed with base = ( 1 - (-4) = 5
Height = 2
Area of Triangle = (1/2) * base * height
= (1/2) * 5 * 2
= 5 sq units
or area of triangles by vertex ( 1 , 0) , ( -4 , 0) and ( 0 , 2)
= (1/2) | 1 ( 0 - 2) - 4( 2 - 0) + 0 (0 - 0) |
= (1/2) | - 2 - 8 |
= (1/2) | - 10 |
= (1/2) (10)
= 5 sq units
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