SOLUTION: Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 12. 10x

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 12. 10x      Log On


   

Question 123357: Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
12. 10x + 2y = 7
y = -5x + 3


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

Start with the given system
10x%2B2y=7
y=-5x%2B3



10x%2B2%28-5x%2B3%29=7 Plug in y=-5x%2B3 into the first equation. In other words, replace each y with -5x%2B3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


10x%2B-10x%2B6=7 Distribute


6=7 Combine like terms on the left side


0=7-6Subtract 6 from both sides


0=1 Combine like terms on the right side


0=1 Simplify

Since this equation is never true for any x value, this means there are no solutions.