Solve graphically the following pair of linear equations: 2x – y = 2, 4x – y = 8. Also, find the areas of the triangles formed by the two lines and: (a) the x-axis; (b) the y-axis.
Answers
Given : 2x – y = 2, 4x – y = 8.
To find : areas of the triangles formed by the two lines and: (a) the x-axis; (b) the y-axis.
Solution:
2x – y = 2,
4x – y = 8.
Intersection
2x = 6 => x = 3
& y = 4
( 3, 4) is the point
(a) the x-axis;
2x – y = 2, Cut at x axis at ( 1 , 0)
4x – y = 8. cut at ax axis at ( 2 , 0 )
Base = ( 2 - 1) = 1
Height = 4 - 0 = 4
Area = (1/2) * 1 * 4 = 2 sq units
(b) the y-axis.
2x – y = 2, Cut at y axis at ( 0 , -2)
4x – y = 8. cut at ax axis at ( 0 , -8 )
Base = -2 -(-8) = 6
Height = 3
Area = (1/2) * 6 * 3 = 9 sq units
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