SOLUTION: please help me solve this equation -4X+2Y=10 -4X-2Y=6

Algebra ->  Expressions-with-variables -> SOLUTION: please help me solve this equation -4X+2Y=10 -4X-2Y=6      Log On


   

Question 324855: please help me solve this equation
-4X+2Y=10
-4X-2Y=6
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%28-4x%2B2y=10%2C-4x-2y=6%29


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


%28-4x%2B2y%29%2B%28-4x-2y%29=%2810%29%2B%286%29


%28-4x%2B-4x%29%2B%282y%2B-2y%29=10%2B6 Group like terms.


-8x%2B0y=16 Combine like terms.


-8x=16 Simplify.


x=%2816%29%2F%28-8%29 Divide both sides by -8 to isolate x.


x=-2 Reduce.


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


-4x%2B2y=10 Now go back to the first equation.


-4%28-2%29%2B2y=10 Plug in x=-2.


8%2B2y=10 Multiply.


2y=10-8 Subtract 8 from both sides.


2y=2 Combine like terms on the right side.


y=%282%29%2F%282%29 Divide both sides by 2 to isolate y.


y=1 Reduce.


So the solutions are x=-2 and y=1.


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 -4x%2B2y=10 (red) and -4x-2y=6 (green)