**Definition**1.5. 2 A system of linear equations is called

**inconsistent**if it has no solutions. A system which has a solution is called

**consistent**. If a system is

**inconsistent**, a REF obtained from its augmented matrix will include a row of.

Moreover, are parallel lines consistent or inconsistent?

A system of **parallel lines** can be **inconsistent** or **consistent** dependent. If the **lines** in the system have the same slope but different intercepts then they are just **inconsistent**. Though if they have the same slope and intercepts (in other words, they are the same line) then they are **consistent** dependent.

Also, what does it mean to be consistent? Someone who is **consistent** always behaves in the same way, has the same attitudes towards people or things, or achieves the same level of success in something. If one fact or idea is **consistent** with another, they **do** not contradict each other.

Also to know is, what does it mean for a linear system to be consistent?

In mathematics and in particularly in algebra, a **linear** or nonlinear **system** of equations is called as **consistent** if there is at least one set of values for the unknowns that satisfies each equation in the **system**—that is, that when substituted into each of the equations **makes** each equation hold true as an identity.

What does consistent mean in matrices?

A system which has a solution **is** called **consistent**. If a system **is inconsistent**, a REF obtained from its augmented **matrix** will include a row of. the form 0 0 0 0 1, i.e. will have a leading 1 in its rightmost column.

###
How do you know if a system is consistent?

**If a system**has at least one solution, it is said to be

**consistent**.

**If**a

**consistent system**has exactly one solution, it is independent .

**If**a

**consistent system**has an infinite number of solutions, it is dependent .

**When**you graph the equations, both equations represent the same line.

###
What does an inconsistent matrix look like?

**matrix**is

**inconsistent**if and only if it has a row that

**looks like**0 0 0 … 0 1. There exist infinite number of values of and that satisfy the linear system of equations represented by this augmented

**matrix**. In both cases, the augmented

**matrix**is

**CONSISTENT**.

###
How do you know if a system is consistent inconsistent or dependent without graphing?

**Without**”

**Graphing**.

**If**slopes are different,

**system**is independent.

**If**slopes are same and intercepts are same,

**system**is

**dependent**.

**If**slopes are same and intercepts are

**not**the same,

**system**is

**inconsistent**.

###
What is Cramer’s rule matrices?

**Cramer’s Rule**for a 2×2 System (with Two Variables)

**Cramer’s Rule**is another method that can solve systems of linear equations using determinants. In terms of notations, a

**matrix**is an array of numbers enclosed by square brackets while

**determinant**is an array of numbers enclosed by two vertical bars.

###
What does infinitely many solutions look like?

**is**when we have

**what is**called

**infinite solutions**. This happens when all numbers

**are solutions**. This situation means that there

**is**no one

**solution**. The equation 2x + 3 = x + x + 3

**is**an example of an equation that has an

**infinite**number of

**solutions**.

###
How do you solve a system without graphing?

**solve a system**of linear equations

**without graphing**, you can use the substitution method. This method works by

**solving**one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and

**solving**for the other variable.

###
How do you determine if a system of equations has a unique solution?

**system**of linear

**equations has a unique solution**(the trivial

**solution**)

**if**and only

**if**its determinant is non-zero.

**If**this determinant is zero, then the

**system has**an infinite number of solutions.

###
How do you know if a linear equation has infinite solutions?

**linear equation has infinitely**many

**solutions**(in the variable x)

**if**and only

**if**both the overall coefficients of x on the two sides are equal, and the overall constants on the two sides are equal.

###
What is an example of an inconsistent equation?

**inconsistent equations**. noun.

**Inconsistent equations**is defined as two or more

**equations**that are impossible to solve based on using one set of values for the variables. An

**example**of a set of

**inconsistent equations**is x+2=4 and x+2=6.

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