Question

Represent the following system of linear equations graphically. From the graph, find the points, where the lines intersect y-axis:
$3x+y-5=0,2x-y-5=0.$

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 − 5 = 0

3x + y − 5 = 0
⇒ y = (−3x + 5) ...........(i)
Putting x = 0, we get y = 5.
Putting x = 1, we get y = 2.
Putting x = 2, we get y = −1.
Thus, we have the following table for the equation 3x + y − 5 = 0.

x	0	1	2
y	5	2	−1

Now, plot the points A(0, 5), B(1 , 2) and C(2, −1) on the graph paper.
Join AB and BC to get the graph line AC. Extend it on both ways.
Thus, AC is the graph of 3x + y − 5 = 0.

Graph of 2x − y − 5 = 0
2x − y − 5 = 0
⇒ y = (2x − 5) ............(ii)
Putting x = 0, we get y = −5.
Putting x = 1, we get y = −3.
Putting x = 3, we get y = 1.
Thus, we have the following table for the equation 2x − y − 5 = 0.

x	0	1	3
y	−5	−3	1

Now, plot the points P(0, −5), Q(1, −3) and R( 3, 1) on the same graph paper. Join PQ and QR to get the graph line PR. Extend it on both ways.
Then, PR is the graph of the equation 2x − y − 5 = 0.

Hence, the lines (i) and (ii) intersect y-axis at (0, 5) and (0, −5), respectively.