A solution to a system of linear equations in two variables is an ordered pair that.

If there is at least one combination of values for the unknowns that satisfies each equation in the system—that is, makes each equation hold true as an identity—then a system of equations, whether linear or nonlinear, is said to be consistent.

When is the system of equations is said to be non-consistent?

If there isn't a set of values for the unknowns that solves every equation, then the system of equations is said to be inconsistent.

Ex: Consider a system of linear equations:

x+3y=6

x=-3y+6 …..(1)

2x+8y= -12 …..(2)

Substitute equation (1) in (2)

2(-3y+6)+8y=-12

-6y+12+8y=-12

2y=-24

y=-12 ….(3)

Substitute equation (3) in (1)

x+3(-12)=6

x-36=6

x=42

Here, the order pair (x,y)=(42,-12) is the solution of the given linear equations and satisfy equations (1) and (2)

> 42+3(-12) = 42-36 .....From (1)

= 6 = RHS

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