SOLUTION: Solve the system by substitution x+y=12 y=2x y=12+x Need to solve and graph, the second equation is confusing as to how it fits into the first equation.

Algebra ->  Equations -> SOLUTION: Solve the system by substitution x+y=12 y=2x y=12+x Need to solve and graph, the second equation is confusing as to how it fits into the first equation.      Log On


   

Question 127072This question is from textbook Beginning Algebra
: Solve the system by substitution
x+y=12
y=2x
y=12+x
Need to solve and graph, the second equation is confusing as to how it fits into the first equation. This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
x%2By=12
y=2x



x%2B2x=12 Plug in y=2x into the first equation. In other words, replace each y with 2x. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


3x=12 Combine like terms on the left side


x=%2812%29%2F%283%29 Divide both sides by 3 to isolate x



x=4 Divide




Now that we know that x=4, we can plug this into y=2x to find y



y=2%284%29 Substitute 4 for each x


y=8 Simplify


So our answer is x=4 and y=8 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+12-x%2C+2x%29+ Graph of x%2By=12 (red) and y=2x (green)