Systems of Linear Equations: Definitions

A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Think back to linear equations. For instance, consider the linear equation y = 3x – 5. A "solution" to this equation was any x, y-point that "worked" in the equation. So (2, 1) was a solution because, plugging in 2 for x:
3x – 5 = 3(2) – 5 = 6 – 5 = 1 = y
On the other hand, (1, 2) was not a solution, because, plugging in 1 for x:
3x – 5 = 3(1) – 5 = 3 – 5 = –2
...which did not equal y (which was 2, for this point). Of course, in practical terms, you did not find solutions to an equation by picking random points, plugging them in, and checking to see if they "work" in the equation. Instead, you picked x-values and then calculated the corresponding y-values. And you used this same procedure to graph the equation. This points out an important fact: Every point on the graph was a solution to the equation, and any solution to the equation was a point on the graph.
Now consider the following two-variable system of linear equations:
y = 3x – 2
y = –x – 6
Category:Math dictionary