Substitution Method

if you are given a problem in which there are 2 variables and 2 equations, there are many ways to solve for the variables. One method is called the method of substitution.

for instance if your two equations are:
1) x+2y=8
2)2x+6y=20
You can use the method of substitution----------

Steps:

1) 2y=7-x (by subtracting x from both sides)
2) y=4-0.5x (dividing both sides of the equation by two)
3) We can plug (4-0.5x) back into the 2nd equation to get:
4) 2x +6(4-0.5x)=20 (because y is equal to 4-0.5x, we can plug that y value into the 2nd equation)
5)2x+24-3x=20 (using the distributive property)
6) -x+24=20 (combining like terms)
7)-x=-4 (subtract 24 from both sides of the equation)
8)x=4 (multiply everything by -1)
Now, you can plug the x value into either one of the original equations.
9) (4)+2y=8 (the x value of 4 was plugged into equation #1)
10)2y=4 (subtract 4 from each side)
11) y=2 (divide both sides of the equation by 2)
Now, you have figured out both your X and Y value. To check this answer you can plug both values into either equation and see if it matches the given outcome.
12) (4)+2(2)=8 (the X and Y values were plugged in)
13) 8=8 (your answer has been checked!!)