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# Solve the equations graphically and find the vertices and the area of the triangle formed by these lines and the y-axis: 2x-5y+4=0, 2x+y-8=0

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Sir please give me a detailed solution of this question as it was already asked in previous year paper of 2010 in which we have given that 2x-5y+4=0, 2x+y-8=0 and we have to solve the equations graphically and also asked to find the vertices and also the area of the triangle formed by these lines and the y-axis

RS Aggarwal, Class 10, chapter 3A, question no 19

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1. Given equations are
2x5y+4=0...(1)
2x+y8=0...(2)

Write y in terms of x for equation (1).
2x5y+4=0
y=(2x+4)/5
Substitute different values of x in the above equation to get corresponding values of y

For  x=2,y=0
For  x=3,y=2
For  x=7,y=2

Now plot the points A(2,0), B(3,2) and C(7,2) in the graph paper and join A, B and C to get the graph of 2x5y+4=0

Similarly, Write y in terms of x for equation (2).
2x+y8=0
y=82x
Substitute different values of x in the above equation to get corresponding values of y

For  x=4,y=0
For  x=3,y=2
For  x=2,y=4

Now plot the points D(4,0), E(3,2) and F(2,4) in the graph paper and join D, E and F to get the graph of 2x+y8=0

From the graph:
Both the lines intersect each other at point E(3,2) and y-axis at G(0,54) and H(0,8)
[Co-ordinates of point G and H are obtained from graph or put x=0 in equation (1) and (2)]

Area of HGE=21(base×altitude)
=1/2×(7 1/4)×3 sq.units
=1/2×(29/4)×3 sq.units
=87/8 sq.units
=10.875 sq.units.

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