SOLUTION: Solve the system of equations. x + 5y = 2 -6x + 5y = -47

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Question 241421: Solve the system of equations.
x + 5y = 2
-6x + 5y = -47
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%2B5y=2%2C-6x%2B5y=-47%29


-1%28-6x%2B5y%29=-1%28-47%29 Multiply the both sides of the second equation by -1.


6x-5y=47 Distribute and multiply.


So we have the new system of equations:
system%28x%2B5y=2%2C6x-5y=47%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:


%28x%2B5y%29%2B%286x-5y%29=%282%29%2B%2847%29


%28x%2B6x%29%2B%285y%2B-5y%29=2%2B47 Group like terms.


7x%2B0y=49 Combine like terms.


7x=49 Simplify.


x=%2849%29%2F%287%29 Divide both sides by 7 to isolate x.


x=7 Reduce.


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x%2B5y=2 Now go back to the first equation.


7%2B5y=2 Plug in x=7.


5y=2-7 Subtract 7 from both sides.


5y=-5 Combine like terms on the right side.


y=%28-5%29%2F%285%29 Divide both sides by 5 to isolate y.


y=-1 Reduce.


So the solutions are x=7 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%2B5y=2 (red) and -6x%2B5y=-47 (green)