SOLUTION: Please solve each system -8x - 7y =2 7x + 6y = -1

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Question 374764: Please solve each system
-8x - 7y =2
7x + 6y = -1
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%28-8x-7y=2%2C7x%2B6y=-1%29


6%28-8x-7y%29=6%282%29 Multiply the both sides of the first equation by 6.


-48x-42y=12 Distribute and multiply.


7%287x%2B6y%29=7%28-1%29 Multiply the both sides of the second equation by 7.


49x%2B42y=-7 Distribute and multiply.


So we have the new system of equations:
system%28-48x-42y=12%2C49x%2B42y=-7%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:


%28-48x-42y%29%2B%2849x%2B42y%29=%2812%29%2B%28-7%29


%28-48x%2B49x%29%2B%28-42y%2B42y%29=12%2B-7 Group like terms.


x%2B0y=5 Combine like terms.


x=5 Simplify.


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-48x-42y=12 Now go back to the first equation.


-48%285%29-42y=12 Plug in x=5.


-240-42y=12 Multiply.


-42y=12%2B240 Add 240 to both sides.


-42y=252 Combine like terms on the right side.


y=%28252%29%2F%28-42%29 Divide both sides by -42 to isolate y.


y=-6 Reduce.


So the solutions are x=5 and y=-6.


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 -8x-7y=2 (red) and 7x%2B6y=-1 (green)