Given : - 

Two equation 2x – y = 5 and 4x – 2y = 7 

Tip : - We know that 

For a system of 2 simultaneous linear equation with 2 unknowns 

(i) If D ≠ 0, then the given system of equations is consistent and has a unique solution given by

x = \(\frac{D_1}{D}\), y = \(\frac{D_2}{D}\)

(ii) If D = 0 and D₁ = D₂ = 0, then the system is consistent and has infinitely many solution. 

(iii) If D = 0 and one of D₁ and D₂ is non – zero, then the system is inconsistent.

Now, 

We have, 

2x – y = 5 

4x – 2y = 7 

Lets find D

⇒ D = \(\begin{vmatrix}2& -1 \\[0.3em]4 &-2 \\[0.3em]\end{vmatrix}\) 

⇒ D = – 4 + 4 

⇒ D = 0 

Again, 

D₁ by replacing 1^st column by B 

Here,

B = \(\begin{vmatrix}5 \\[0.3em]7\\[0.3em]\end{vmatrix}\)

⇒ D₁ = \(\begin{vmatrix}5& -1 \\[0.3em]7 &-2 \\[0.3em]\end{vmatrix}\) 

⇒ D₁ = – 10 + 7 

⇒ D₁ = – 3

And, 

D₂ by replacing 2^nd column by B 

Here,

B = \(\begin{vmatrix}5 \\[0.3em]7\\[0.3em]\end{vmatrix}\)

⇒ D₂ = \(\begin{vmatrix}2& 5 \\[0.3em]4 &7 \\[0.3em]\end{vmatrix}\) 

⇒ D₂ = 14 – 20 

⇒ D₂ = – 6

So, here we can see that 

D = 0 and D₁ and D₂ are non – zero 

Hence the given system of equation is inconsistent.