|Systems of Equations|
Two or more equations put together are called Systems of Equations.
Below, we have a system of equations:
2y = x + 1
3x = 4y - 1
The solution of a system of equations is called an ordered pair (x, y).
Below are examples of some of the linear and quadratic functions we've already learned about:
Quadratic systems are sets of quadratic equations that have variables with the same values. For example:
The solution of a system of equations is called an ordered pair (x, y). There may be multiple (or no) solutions.
The above system has a solution at (0, -4).
The above system has two solutions at roughly (0, -0.2) and (5, 2.8).
The above system has no solutions.
Let's solve the system of equations below:
To graph, first we must convert both equations to slope-intercept form:
Now, we graph the equations:
This system of equations has no solution.