Question

Solve the following system of linear equations graphically:
$2x-5y+4=0,2x+y-8=0.$
Find the points, were these lines meet 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 2x − 5y + 4 = 0
2x − 5y + 4 = 0
⇒ 5y = (2x + 4)
∴ $y=\frac{2x+4}{5}$ ............(i)
Putting x = 3, we get y = 2.
Putting x = −2, we get y = 0.
Putting x = 8, we get y = 4.
Thus, we have the following table for the equation 2x − 5y + 4 = 0.

x	−2	3	8
y	0	2	4

Now, plot the points A(−2, 0), B( 3, 2) and C(8, 4) 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 2x − 5y + 4 = 0.

Graph of 2x + y − 8 = 0
2x + y − 8 = 0
⇒ y = (−2x + 8) ............(ii)
Putting x = 3, we get y = 2.
Putting x = 1, we get y = 6.
Putting x = 2, we get y = 4.
Thus, we have the following table for the equation 2x + y − 8 = 0.

x	1	3	2
y	6	2	4

Now, plot the points P(1, 6), Q(2, 4). The point B(3, 2) has already been plotted. Join PQ and QB to get the graph line PB. Extend it on both ways.
Then, PB is the graph of the equation 2x + y − 8 = 0.

The two graph lines intersect at B(3, 2).
∴ The solution of the given system of equations is x = 3 and y = 2.
These graph lines intersect the y-axis at R(0,0.8) and S(0, 8).