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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
2xâˆ’5y+4=0...(1)
2x+yâˆ’8=0...(2)

WriteÂ yÂ in terms ofÂ xÂ for equationÂ (1).
2xâˆ’5y+4=0
â‡’y=(2x+4)/5â€‹
Substitute different values ofÂ xÂ in the above equation to get corresponding values ofÂ y

ForÂ Â x=âˆ’2,y=0
ForÂ Â x=3,y=2
ForÂ Â x=âˆ’âˆ’7,y=âˆ’2

Now plot the pointsÂ A(âˆ’2,0),Â B(3,2)Â andÂ C(âˆ’7,âˆ’2)Â in the graph paper and joinÂ A,Â BÂ andÂ CÂ to get the graph ofÂ 2xâˆ’5y+4=0

Similarly, WriteÂ yÂ in terms ofÂ xÂ for equationÂ (2).
2x+yâˆ’8=0
â‡’y=8âˆ’2x
Substitute different values ofÂ xÂ in the above equation to get corresponding values ofÂ y

ForÂ Â x=4,y=0
ForÂ Â x=3,y=2
ForÂ Â x=2,y=4

Now plot the pointsÂ D(4,0),Â E(3,2)Â andÂ F(2,4)Â in the graph paper and joinÂ D,Â EÂ andÂ FÂ to get the graph ofÂ 2x+yâˆ’8=0

From the graph:
Both the lines intersect each other at pointÂ E(3,2)Â andÂ y-axis atÂ G(0,54â€‹)Â andÂ H(0,8)
[Co-ordinates of pointÂ GÂ andÂ HÂ are obtained from graphÂ orÂ putÂ x=0Â in equationÂ (1)Â andÂ (2)]

âˆ´Â Area ofÂ â–³HGE=21â€‹(baseÃ—altitude)
=1/2â€‹Ã—(7 1/4â€‹)Ã—3Â sq.units
=1/2Ã—(29/4â€‹)Ã—3Â sq.units
=87/8â€‹Â sq.units
=10.875Â sq.units.

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