Question

Draw the graph of the following equations:
$3x+y-11=0\mathrm{and}x-y-1=0.$
Shade the region bounded by these lines and the y-axis.

Answer 1

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis respectively.
Graph of 3x + y - 11= 0

3x + y = 11
⇒ y = (11- 3x) ...........(i)
Putting x = 2, we get y = 5.
Putting x = 3, we get y = 2.
Putting x = 5, we get y = - 4.
Thus, we have the following table for the equation 3x + y = 11:

x	2	3	5
y	5	2	-4

Now, plots the points A(2, 5) , B(3, 2) and C(5, - 4) on the graph paper.
Join AB and BC to get the graph line AC. Extend it both ways.
Thus, line AC is the graph of 3x + y = 11.

Graph of x − y = 1
x − y = 1
⇒ y = (x - 1) .............(ii)
Putting x = −3, we get y = −4.
Putting x = 0, we get y = - 1.
Putting x = 3, we get y = 2.
Thus, we have the following table for the equation x − y = 1:

x	−3	0	3
y	−4	-1	2

Now, plots the points P(-3, -4) and Q(0, −1). The point B(3, 2) has already been plotted. Join PQ and QB and extend it both ways.
Thus, line PB is the graph of x − y = 1.

The two graph lines intersect at B(3 , 2).
∴ x = 3 and y = 2 is the solution of the given system of equations.
The region bounded by these lines and the y - axis has been shaded.