List the three methods for solving equations and give a brief explanation of each method.

Method 1: Graphing
This method requires you to graph both equations to see the points of intersection. If you're solving two linear lines, they will only intersect once, meaning there is only one point at which there lies an intersection.

This method is slow when dealing with more complex equations that you can't graph at first, and requires a higher knowledge in sketching graphs in mathematics.

Method 2: Substitution
This method is a process whereby you solve for one variable in one of your systems of equations, and placing the first equation in place of any variable in order to "substitute". This eliminates one of the variables, leaving the other variable easy to solve. Upon doing so, you can easily find the solution to both unknown variables.

This is generally easier when given harder linear lines to sketch, and thus, is generally more accepted than graphing.

Method 3: Elimination
This method requires you to "eliminate" a variable by either adding or subtracting both equations together. Like method 2, this will allow you to solve for one variable, because you would have eliminated the other variable when adding or subtracting the two equations together.

This is harder when the two variables' coefficients are different, so using elimination can sometimes be harder than using substitution.

6(2x + 5y)6 (2x) = 12x6 (5y) = 30y12x + 30y