SOLUTION: Solve each system by addition x-2y=-1 -x+5y=4 and 3x+5y=-11 x-2y=11

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Question 175920: Solve each system by addition
x-2y=-1
-x+5y=4
and
3x+5y=-11
x-2y=11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you going in the right direction


# 1




Start with the given system of equations:
system%28x-2y=-1%2C-x%2B5y=4%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-2y%29%2B%28-x%2B5y%29=%28-1%29%2B%284%29


%28x-x%29%2B%28-2y%2B5y%29=-1%2B4 Group like terms.


0x%2B3y=3 Combine like terms. Notice how the x terms cancel out.


3y=3 Simplify.


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


y=1 Reduce.


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


x-2y=-1 Now go back to the first equation.


x-2%281%29=-1 Plug in y=1.


x-2=-1 Multiply.


x=-1%2B2 Add 2 to both sides.


x=1 Combine like terms on the right side.


So our answer is x=1 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 x-2y=-1 (red) and -x%2B5y=4 (green)