System of Equations

System of Equations

A finite set of equations that can be verified simultaneously.

A system of equations in two variables can be represented in a Cartesian plane using the graph of each equation. The points of intersection of these graphs are the solutions to the system.

Example

Consider the following system of equations:

$$\left\{\begin{matrix} y=2x\\ y=4x^2-1 \end{matrix}\right.$$

The solutions to this system are the ordered pairs of coordinates ($$\frac{(1+\sqrt{5})}{4}$$, $$\frac{(1+\sqrt{5})}{2}$$)
and ($$\frac{(1-\sqrt{5})}{4}$$, $$\frac{(1-\sqrt{5})}{2}$$).