SOLUTION: I am not sure how to solve this system x + y = -4 -x-5y=-8

Algebra ->  Expressions-with-variables -> SOLUTION: I am not sure how to solve this system x + y = -4 -x-5y=-8      Log On


   

Question 548770: I am not sure how to solve this system
x + y = -4
-x-5y=-8
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve this system
x + y = -4
-x-5y=-8
-------------
Add to get -4y = -12
y = 3
----
Solve for "x":
x + y = -4
x + 3 = -4
x = -7
----
Solution: (-7,3)
==================
Cheers,
Stan H.
==================

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%2By=-4%2C-x-5y=-8%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%2By%29%2B%28-x-5y%29=%28-4%29%2B%28-8%29


%28x-x%29%2B%28y-5y%29=-4%2B-8 Group like terms.


0x-4y=-12 Combine like terms.


-4y=-12 Simplify.


y=%28-12%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=3 Reduce.


------------------------------------------------------------------


x%2By=-4 Now go back to the first equation.


x%2B3=-4 Plug in y=3.


x=-4-3 Subtract 3 from both sides.


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


So the solutions are x=-7 and y=3.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of x%2By=-4 (red) and -x-5y=-8 (green)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim