There are three ways to solve systems of two equations with two variables.
y=3x-12 3x+3(3x-12)=12 3x+9x-36=12 12x-36=12 12x=48 x=4
y=3(4)-12 y=12-12 y=0
Ex. 2x+4y=4 and -2x+2y=8
(2x=4y=4)+(-2x+2y=8) 6y=12 y=2
-2x+2(2)=8 -2x+4=8 -2x=4 x=-2
- Graphing: you make a graph of the two equations and find the point where they intersect. Simple.
- Substitution: you get a variable by itself. Because the first variable equals the rest of the equation, you can insert the equation in place of the variable. Once this is plugged in, you can solve for the remaining variable. After obtaining this variable, you use it to find the first variable, the one you replaced.
y=3x-12 3x+3(3x-12)=12 3x+9x-36=12 12x-36=12 12x=48 x=4
y=3(4)-12 y=12-12 y=0
- Elimination: you must find a way to multiply the equations so that you have one variable that will cancel when the equations are added. Once one variable is eliminated, you are able to solve the remaining equation for the remaining variable. This variable can then be plugged in to find the originally eliminated variable.
Ex. 2x+4y=4 and -2x+2y=8
(2x=4y=4)+(-2x+2y=8) 6y=12 y=2
-2x+2(2)=8 -2x+4=8 -2x=4 x=-2