Solution:

Given,

x – 2y = 2……. (i)

4x – 2y = 5……. (ii)

For equation (i),

⇒ y = (x – 2)/2

When x = 2, we have y = (2 – 2)/2 = 0

When x = 0, we have y = (0 – 2)/2 = -1

Thus, we have the following table giving points on the line x – 2y = 2

For equation (ii),

We solve for x:

⇒ x = (5 + 2y)/4

So, when y = 0

x = (5 + 2(0))/4 = 5/4

And, when y = 1.5

⇒ x = (5 + 2(1))/4 = 7/4

Thus, we have the following table giving points on the line 4x – 2y = 5

Graph of the equations (i) and (ii) is as below:

It is clearly seen that the two lines intersect at (1,0).

Hence, the system of equations is consistent.