SOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
In this section we’ll learn to solve systems of equations.
It’s important that we understand just exactly what is
meant by a solution of a system of equations.
The equations in the system represent lines in a plane.
The
solution of the system is the result of graphing both lines in the plane.
Those lines may be parallel; they may be
different names for the same line; or the lines may intersect in one point.
Those are the only possible solutions.
Most of the time, the lines will meet in a single point and the solution is an ordered pair.
In order to be a solution to a system, the ordered pair must satisfy both equations.
Consider
5
4
34
2
8
x
y
x
y
.
Is (0, 3) a solution of this system?