Suppose you are given three equations forming a linear system. Explain how you could determine whether the sys

Question

Suppose you are given three equations forming a linear system. Explain how you could determine whether the system is consistent or inconsistent. Give an example.

Answer 1

Inconsistent equations have no simultaneous solution. An example would be
3x + 4y - 5z =4
and
3x +4y -5z = 8
Two equal items should equal the same thing in a consistent system.

Answer 2

It relies upon what proportion variables are there. If there are 3 variables in 3 equations, then eliminate between the variable it could have been common in case you could have given 3 equations. e.g. equations are a + b + c = fifty 4 --------a million a + b = 27 ----------2 a + c = 39 ----------3 right here the two putting fee of a + b from eq. 2 or fee of (a + c) in eq. a million you will locate the two fee of b or c via putting a + b = 27 in eq. a million 27 + c = fifty 4 or c = 27 positioned this fee in eq. 3 a + 27 = 39 or a = 12 putting this fee in eq. 2 12 + b = 27 or b = 15 in this way you will locate the values of a, b and c a = 12, b = 15 and c =27