is it consistant, inconsistant, or depent

## 2x+5y=-21/-4-10y=42

# 1 Answer

Notice that this is a system of linear equations, for which we can solve for as follows:

2x + 5y = -21 ==> 2ยท(2x + 5y = -21) ==> **4x + 10y = -42**

-4x - 10y = 42 ==> ==> ==> **-4x - 10y = 42**

Combining these two equations we arrive at the following:

4x + 10y = -42

-4x - 10y = 42

_________________________

4x - 4x + 10y - 10y = -42 + 42 ==> **0 = 0**

When you arrive at an answer that is an identity (e.g., 0 = 0), this indicates that the equations are identical or equivalent. This means that the lines are the same and they intersect at infinitely many points; that is, there are infinitely many solutions to this system of equations.

When a system of equations has *no solutions*, then the system in *inconsistent*. If it has
*one or more solutions* (i.e., *infinitely many solutions*), then it is
*consistent*. When the *solution to one equation in the system is the solution to the other equation* in the system, then the
*equations are identical* and the system is *dependent*. If the system has
*one unique solution*, then the system is *independent*.

Since we've found that the system has infinitely many solutions and the equations are identical, then this system of equations is consistent and dependent.