Question

Show graphically the systems of equations is in-consistent (i.e has no solution):

3x – 5y = 20 

6x – 10y = – 40

Answer 1

Given, 

3x – 5y = 20……. (i) 

6x – 10y = – 40……. (ii) 

For equation (i), 

⇒ y = \(\frac{(3x – 20)}{5}\)

When x = 5, we have y = \(\frac{(3(5) – 20)}{5}\) = -1 

When x = 0, we have y = \(\frac{(3(0) – 20)}{5}\) = -4 

Thus we have the following table giving points on the line 3x – 5y = 20

x	5	0
y	-1	-4

For equation (ii), 

We solve for y: 

⇒ y = \(\frac{(6x + 40)}{10}\) 

So, when x = 0 

y = \(\frac{(6(0) + 40)}{10}\) = 4 

And, when x = -5 

⇒ y = (6(-5) + 40)/10 = 1 

Thus we have the following table giving points on the line 6x – 10y = – 40

x	0	-5
y	4	1

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

It is clearly seen that, there is no common point between these two lines. 

Hence, the given systems of equations is in-consistent.