Question

Show graphically that the system of equations $x-2y=2,4x-2y=5$ is consistent.

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 x − 2y = 2
x − 2y = 2
⇒ 2y = (x − 2)
∴ $y=\frac{x-2}{2}$.........(i)
Putting x = 0, we get y = −1.
Putting x = 2, we get y = 0.
Putting x = 1, we get y = −0.5.
Thus, we have the following table for the equation x − 2y = 2.

x	0	2	1
y	−1	0	−0.5

Now, plot the points A(0, −1), B( 2, 0) and C(1, −0.5) on the graph paper.
Join AC and BC to get the graph line AB. Extend it on both ways.
Thus, AB is the graph of x − 2y = 2.

Graph of 4x − 2y = 5
4x − 2y = 5
⇒ 2y = (4x − 5)
∴ $y=\frac{4x-5}{2}$...........(ii)
Putting x = 0, we get y = −2.5.
Putting x = 1, we get y = −0.5.
Putting x = 2, we get y = 1.5.
Thus, we have the following table for the equation 4x − 2y = 5.

x	0	1	2
y	−2.5	−0.5	1.5

Now, plot the points P(0, −2.5) and Q(2, 1.5). The point C(1, −0.5) has already been plotted. Join PC and CQ to get the graph line PQ. Extend it on both ways.
Then, PQ is the graph of the equation 4x − 2y = 5.

The two graph lines intersect at C(1, −0.5).
Hence, the given system of equations is consistent.