SOLUTION: Solve the following system of equations. Please show your work. x - y = 16 2x + y = 2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following system of equations. Please show your work. x - y = 16 2x + y = 2      Log On


   

Question 325252: Solve the following system of equations. Please show your work.
x - y = 16
2x + y = 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x-y=16%2C2x%2By=2%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x-y%29%2B%282x%2By%29=%2816%29%2B%282%29


%28x%2B2x%29%2B%28-y%2By%29=16%2B2 Group like terms.


3x%2B0y=18 Combine like terms.


3x=18 Simplify.


x=%2818%29%2F%283%29 Divide both sides by 3 to isolate x.


x=6 Reduce.


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x-1y=16 Now go back to the first equation.


6-1y=16 Plug in x=6.


-y=16-6 Subtract 6 from both sides.


-y=10 Combine like terms on the right side.


y=%2810%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=-10 Reduce.


So the solutions are x=6 and y=-10.


Which form the ordered pair .


This means that the system is consistent and independent.