# What does it mean when a system is consistent?

To sum up, a

**consistent system**has at least one solution. An inconsistent**system**has NO solution at all. Now for the other pair. " Dependent" versus "Independent." When a**system**is "dependent," it**means**that ALL points that work in one of them ALSO work in the other one.A.

### How can you tell if a system is consistent or inconsistent?

**If**a

**consistent system**has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

**If a system**has no solution, it is said to be

**inconsistent**. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

#### What is an inconsistent equation?

A system of**equations**which has no solutions. Note: Attempts to solve**inconsistent**systems typically result in impossible statements such as 0 = 3. See also. Consistent system of**equations**, overdetermined system of**equations**, underdetermined system of**equations**, linear system of**equations**.#### What is the solution to the system?

In this case the two**equations**describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the**equation**of either line. Thus the pair (x, y) is the one and only**solution to the system of equations**.#### How many solutions are in a parallel line?

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is**one solution**that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

B.

### When a system of two linear equations is inconsistent?

Since parallel lines never

**cross**, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution. The third graph above, "Case 3", appears to show only one line.#### How many solutions does a system of linear equations have if it is consistent?

A system of two linear equations can have**one solution**, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. 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 .#### How can you find the solution of a system of linear equations by graphing?

The**solution**of such a**system**is the ordered pair that is a**solution**to both**equations**. To**solve**a**system**of**linear equations**graphically we**graph**both**equations**in the same coordinate**system**. The**solution**to the**system**will be in the point where the**two**lines intersect.#### What does it mean to be a solution to a system of equations?

In this case the two**equations**describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the**equation**of either line. Thus the pair (x, y) is the one and only**solution**to the**system of equations**.

C.

### What is a dependent system of linear equations?

A

**system of equations**is called an inconsistent**system of equations**if there is no solution because the lines are parallel. A**dependent system of equations**is when the same line is written in two different forms so that there are infinite solutions.#### How do you find the solution to a system of equations?

There can be zero solutions,**1 solution**or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.#### Which are methods used to solve linear systems?

**There are three ways to solve systems of linear equations in two variables:**- graphing.
- substitution method.
- elimination method.

#### What does the intersection of the two graphs mean?

Remember, the**graph**of a line represents every point that is a possible solution for the equation of that line. So when the**graphs**of**two**equations cross, the point of**intersection**lies on both lines, meaning that it is a possible solution for both equations.

Updated: 21st November 2019