How do you solve x+y=5 and 3x+y=15 using the substitution method?

Oct 30, 2014

In order to solve this dual equation system we can use the substitution method since at least one of the variable has a leading coefficient of 1.

Begin with the simpler equation x + y = 5

First isolate one of the variables

x + y - y = 5 - y x = 5 - y

Since x = 5 - y we can substitute (5 - y) into the other equation in place of x in 3x + y = 15 to create an equation with a single variable.

3(5 - y) + y = 15 Use distributive property

15 - 3y + y = 15 Combine like terms

15 - 2y - 15 = 15 -15 Subtract 15 from both sides

$\frac{- 2 y}{-} 2 = \frac{0}{-} 2$ Divide by -2 on both sides to isolate the variable

y = 0

Now plug this value in and solve for x.

x = 5 - 0

x= 5

( 5 , 0 ) is the final solution.