How do you solve #x+y=5# and #3x+y=15# using the substitution method?
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
y = 0
Now plug this value in and solve for x.
x = 5 - 0
( 5 , 0 ) is the final solution.