SOLUTION: -4x+y=-5 2x+y=7

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: -4x+y=-5 2x+y=7      Log On


   

Question 173188This question is from textbook algebra2
: -4x+y=-5
2x+y=7 This question is from textbook algebra2

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%2By=-5%2C2x%2By=7%29


2%282x%2By%29=2%287%29 Multiply the both sides of the second equation by 2.


4x%2B2y=14 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2By=-5%2C4x%2B2y=14%29


Now 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%2By%29%2B%284x%2B2y%29=%28-5%29%2B%2814%29


%28-4x%2B4x%29%2B%281y%2B2y%29=-5%2B14 Group like terms.


0x%2B3y=9 Combine like terms. Notice how the x terms cancel out.


3y=9 Simplify.


y=%289%29%2F%283%29 Divide both sides by 3 to isolate y.


y=3 Reduce.


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


-4x%2By=-5 Now go back to the first equation.


-4x%2B3=-5 Plug in y=3.


-4x%2B3=-5 Multiply.


-4x=-5-3 Subtract 3 from both sides.


-4x=-8 Combine like terms on the right side.


x=%28-8%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=2 Reduce.


So our answer is x=2 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 -4x%2By=-5 (red) and 2x%2By=7 (green)