Graphing linear systems
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
{y=2x+4y=3x+2
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
y=2x+4_8?=2⋅2+4
8=8
y=3x+2_
8?=3⋅2+2
8=8
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
{2y−4x=2y=−x+4