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

5xâˆ’yâˆ’7=0...(1)

xâˆ’y+1=0...(2)

WriteÂ yÂ in terms ofÂ xÂ for equationÂ (1).

5xâˆ’yâˆ’7=0

â‡’y=5xâˆ’7

Substitute different values ofÂ xÂ in the above equation to get corresponding values ofÂ y

ForÂ Â x=0,y=âˆ’7

ForÂ Â x=1,y=âˆ’2

ForÂ Â x=2,y=3

Now plot the pointsÂ A(0,âˆ’7),Â B(1,âˆ’2)Â andÂ C(2,3)Â in the graph paper and joinÂ A,Â BÂ andÂ CÂ to get the graph ofÂ 5xâˆ’yâˆ’7=0

Similarly, WriteÂ yÂ in terms ofÂ xÂ for equationÂ (2).

xâˆ’y+1=0

â‡’y=x+1

Substitute different values ofÂ xÂ in the above equation to get corresponding values ofÂ y

ForÂ Â x=âˆ’1,y=0

ForÂ Â x=1,y=2

ForÂ Â x=2,y=3

Now plot the pointsÂ D(âˆ’1,0),Â E(1,2)Â andÂ F(2,3)Â in the graph paper and joinÂ D,Â EÂ andÂ FÂ to get the graph ofÂ xâˆ’y+1=0

From the graph:

Both the lines intersect each other at pointÂ C(2,3)Â andÂ y-axis atÂ A(0,âˆ’7)Â andÂ G(0,1)Â respectively

[Co-ordinate of pointÂ GÂ is obtained from graph]

âˆ´Â Area ofÂ â–³ACG=21â€‹(baseÃ—altitude)

=21â€‹Ã—8Ã—2Â sq.units

=8Â sq.units.