There are several ways to solve systems of linear equations. The most common methods are by graphing, elimination, and substitution. Let's start off with one of the most basic methods, graphing.
---------------Graphing Method---------------
2x + y = 33x + 2y = 6
In order to solve this system using the graphing method, we first have to change the two equations into slope-intercept form.
2x + y = 3 --> y = -2x + 33x + y = 7 --> y = -3x + 7
Then, we graph these two lines. (Attached Below)The solution set of a system of linear equations when graphing is actually the point at which the two lines intersect. So by graphing the two lines, we can obviously see that the solution set of this problem is (4, -5).
---------------Elimination Method---------------
The concept of elimination revolves around the concept of adding two equations. Using an example, let's see what happens when you add equations together.
2x + y = 33x + 2y = 6-----------5x + 3y = 9
Do you see how this works? Now, let's say that the orientation of these two equations were different. What would you do then?
2x + y = 36 - 3x = 2y
If this situation occurs, you have to rearrange it in a way that the form of the equations match. For example, if you have one in standard form, you have to algebraically return the other equation to the same form.
2x + y = 36 - 3x = 2y --> 6 = 3x + 2y --> 3x + 2y = 6
Now that the equations are in the same form, we can begin to solve. However, let's start with a simpler system to demonstrate the concept.
2x - y = 53x + y = 5
The process of elimination involves adding equations in a way that one of the unknown variables disappears. In this first example, let's see what happens when we simply add them right away.
2x - y = 53x + y = 5
