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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: 5x-y-7=0, x-y+1=0

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An important and exam oriented question from linear equations in two variables in which we have given that 5x-y-7=0, x-y+1=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

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3A, question no 20

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### 1 Answer

1. Given equations are
5xy7=0...(1)
xy+1=0...(2)

Write y in terms of x for equation (1).
5xy7=0
y=5x7
Substitute different values of x in the above equation to get corresponding values of y

For  x=0,y=7
For  x=1,y=2
For  x=2,y=3

Now plot the points A(0,7), B(1,2) and C(2,3) in the graph paper and join A, B and C to get the graph of 5xy7=0

Similarly, Write y in terms of x for equation (2).
xy+1=0
y=x+1
Substitute different values of x in the above equation to get corresponding values of y

For  x=1,y=0
For  x=1,y=2
For  x=2,y=3

Now plot the points D(1,0), E(1,2) and F(2,3) in the graph paper and join D, E and F to get the graph of xy+1=0

From the graph:
Both the lines intersect each other at point C(2,3) and y-axis at A(0,7) and G(0,1) respectively
[Co-ordinate of point G is obtained from graph]

Area of ACG=21(base×altitude)
=21×8×2 sq.units
=8 sq.units.

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