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

Given equations are

5x−y−7=0...(1)

x−y+1=0...(2)

Write y in terms of x for equation (1).

5x−y−7=0

⇒y=5x−7

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 5x−y−7=0

Similarly, Write y in terms of x for equation (2).

x−y+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 x−y+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.