A system of linear equation comprises two or more linear
equations. The solution of a linear system is the ordered pair that
is a solution to all equations in the system.
One way of solving a linear system is by graphing. The solution
to the system will then be in the point in which the two equations
intersect.
Example:
Solve the following system of linear equations
The two lines appear to intersect in (2, 8)
It's a good idea to always check your graphical solution
algebraically by substituting x and y in your equations with the
ordered pair
A linear system that has exactly one solution is called a
consistent independent system. Consistent means that the lines
intersect and independent means that the lines are distinct.
Linear systems composes of parallel lines that have the same
slope but different y-intersect do not have a solution since the
lines won't intersect. Linear systems without a solution are called
inconsistent systems.
Linear systems composed of lines that have the same slope and
the y-intercept are said to be consistent dependent systems.
Consistent dependent systems have infinitely many solutions since
the lines coincide.
Video lesson: Solve the linear system
graphically
