**Definition**

A solution to a system of two linear equations with two
unknowns is an ordered pair that makes each of

the equations true .

**Examples**

Decide whether or not the given ordered pairs are
solutions to the system of equations:

Is (5,−1) a solution to the system ?

Is (−1,3) a solution to the system?

Solve each system of equations by graphing the two linear
equations and finding the point(s) they

have in common . Make sure that you check your solution before stating your
conclusion.

A system can have exactly one solution. In this case, the
system is called

consistent and the equations are called **independent**. This happens

x when the two equations graph to lines that intersect at a single point.

A system can have an “ infinite number ” of solutions. In
this case, the

system is called consistent and the equations are called **dependent**.

x This happens when the two equations graph to the same line

A system can have no solution. In this case, the system is
called

**inconsistent** and the equations are called **independent**. This
happens

x when the two equations graph to parallel lines .

**Examples**

For each system, write both equations in **
slope - intercept ** form and decide – without graphing –

whether the system is consistent or inconsistent and whether the equations are
dependent or

Find the solution to the system of equations