SOLUTION: Solve each of the following systems by substitution. 10. 8x – 4y = 16 y = 2x – 4

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve each of the following systems by substitution. 10. 8x – 4y = 16 y = 2x – 4       Log On


   

Question 123355: Solve each of the following systems by substitution.


10. 8x – 4y = 16
y = 2x – 4


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
8x-4y=16
y=2x-4



8x-4%282x-4%29=16 Plug in y=2x-4 into the first equation. In other words, replace each y with 2x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


8x-8x%2B16=16 Distribute


16=16 Combine like terms on the left side


0=16-16Subtract 16 from both sides


0=0 Combine like terms on the right side


0=0 Simplify

Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.