# MATH 237 LINEAR ALGEBRA

**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