SOLUTION: I'm not really clear on how to set up this type of problem. Any insight would be greatly appreciated. x+y=12 y=3x

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I'm not really clear on how to set up this type of problem. Any insight would be greatly appreciated. x+y=12 y=3x      Log On


   

Question 107332This question is from textbook Introductory and Intermediate Algebra
: I'm not really clear on how to set up this type of problem. Any insight would be greatly appreciated. x+y=12
y=3x This question is from textbook Introductory and Intermediate Algebra

Found 2 solutions by ptaylor, Fombitz:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=12-------------------eq1
y=3x----------------------eq2
I think that substituting "y=3x" from eq2 into eq1 is the easiest way to work this problem. If we do that, we get:
x+3x=12 or
4x=12 divide both sides by 4
x=3
From eq2:
y=3x=3*3=9
So:
x=3
and
y=9
We could also subtract eq2 from eq1 and we would get:
x=12-3x add 3x to both sides
x+3x=12-3x+3x or
4x=12 same as before
CK
from eq1
x+y=12
3+9=12
12=12
from eq2
y=3x
9=3*3
9=9

Hope this helps----ptaylor

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2By=12
2.y=3x
You have two equations with two unknowns, a linear system of equations.
You should be able to solve for x and y.
Using equation 2 and substitute into equation 1.
1.x%2By=12
x%2B%283x%29=12
4x=12
x=3
Now substitute into 2.
2.y=3x
y=3%283%29
y=9
Check your answers with your original equations.
1.x%2By=12
3%2B9=12
12=12
True statement. Good answer.
2.y=3x
9=3%283%29
9=9
True statement. Good answer.
x=3 and y=9.