Question

Examine the consistency of the system of equations.

x + 2y = 2

2x + 3y = 3

Answer 1

Let A = `[(1,2),(2,3)]`, X = `[(x),(y)]`, B = `[(2),(3)]`

Then the given system of equations can be written as,

`[(1,2),(2,3)][(x),(y)] = [(2),(3)]`

Now, |A|

= `|(1,2),(2,3)|`

= 3 − 4

= −1 ≠ 0

∴ The given system of equations is consistent.