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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: x-y-5=0, 3x+5y-15=0

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One of the most important and exam oriented question as it was already asked in previous year paper of 2009 in which we have given the equations x-y-5=0, 3x+5y-15=0 and we have to solve the equations graphically and also asked to  find the vertices and the area of the triangle formed by these lines and the y-axis

RS Aggarwal, Class 10, chapter 3A, question no 18

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1. Given equations are
xy5=0...(1)
3x+5y15=0...(2)

Write y in terms of x for equation (1).
xy5=0
y=(x5)
Substitute different values of x in the above equation to get corresponding values of y

For  x=5,y=0
For  x=0,y=5
For  x=1,y=4

Now plot the points A(5,0), B(0,5) and C(1,4) in the graph paper and join A, B and C to get the graph of xy5=0

Similarly, Write y in terms of x for equation (2).
3x+5y15=0
y=(153x)/5
Substitute different values of x in the above equation to get corresponding values of y

For  x=5,y=0
For  x=0,y=3
For  x=5,y=6

Now plot the points D(5,0), E(0,3) and F(5,6) in the graph paper and join D, E and F to get the graph of 3x+5y15=0

From the graph:
Both the lines intersect each other at point A(5,0) and y-axis at B(0,5) and E(0,3) respectively

Area of BAE=21(base×altitude)
=1/2×8×5 sq.units
=20 sq.units.

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