SOLUTION: Given the system of equations {{{system(x-4y=-12,y=-4+2x)}}} Solve the system of equations using the substitution method.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Given the system of equations {{{system(x-4y=-12,y=-4+2x)}}} Solve the system of equations using the substitution method.      Log On


   

Question 172785: Given the system of equations


system%28x-4y=-12%2Cy=-4%2B2x%29


Solve the system of equations using the substitution method.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

As the name implies, substitution simply involves you "substituting" one variable in for another so that you can solve for that variable.

Let's solve the given system by substitution


Start with the given system
x-4y=-12
y=-4%2B2x



x-4%28-4%2B2x%29=-12 Plug in y=-4%2B2x into the first equation. In other words, replace each y with -4%2B2x. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x%2B16-8x=-12 Distribute


-7x%2B16=-12 Combine like terms on the left side


-7x=-12-16Subtract 16 from both sides


-7x=-28 Combine like terms on the right side


x=%28-28%29%2F%28-7%29 Divide both sides by -7 to isolate x



x=4 Divide




Now that we know that x=4, we can plug this into y=-4%2B2x to find y



y=-4%2B2%284%29 Substitute 4 for each x


y=4 Simplify


So our answer is x=4 and y=4 which forms the ordered pair