SOLUTION: HELLLLPPPP PLEASE....solve using subtraction method 7x + 6y = -5 and -7x + y = 40....type an ordered pair

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Question 550476: HELLLLPPPP PLEASE....solve using subtraction method 7x + 6y = -5 and -7x + y = 40....type an ordered pair
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%287x%2B6y=-5%2C-7x%2By=40%29


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


%287x%2B6y%29%2B%28-7x%2By%29=%28-5%29%2B%2840%29


%287x%2B-7x%29%2B%286y%2B1y%29=-5%2B40 Group like terms.


0x%2B7y=35 Combine like terms.


7y=35 Simplify.


y=%2835%29%2F%287%29 Divide both sides by 7 to isolate y.


y=5 Reduce.


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7x%2B6y=-5 Now go back to the first equation.


7x%2B6%285%29=-5 Plug in y=5.


7x%2B30=-5 Multiply.


7x=-5-30 Subtract 30 from both sides.


7x=-35 Combine like terms on the right side.


x=%28-35%29%2F%287%29 Divide both sides by 7 to isolate x.


x=-5 Reduce.


So the solutions are x=-5 and y=5.


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 7x%2B6y=-5 (red) and -7x%2By=40 (green)


So again, the answer is the ordered pair (-5, 5)