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Examine the consistency of the system of equations. x + 2y = 2 2x + 3y = 3 - Mathematics

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Question

Examine the consistency of the system of equations.

x + 2y = 2

2x + 3y = 3

Sum
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Solution

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.

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Chapter 4: Determinants - Exercise 4.6 [Page 136]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 4 Determinants
Exercise 4.6 | Q 1 | Page 136

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