SOLUTION: Find the values of x and y that solve the following systems of equations. 6x+7y=-5 4x+3y=-15

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Question 181961: Find the values of x and y that solve the following systems of equations.
6x+7y=-5
4x+3y=-15
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%286x%2B7y=-5%2C4x%2B3y=-15%29


2%286x%2B7y%29=2%28-5%29 Multiply the both sides of the first equation by 2.


12x%2B14y=-10 Distribute and multiply.


-3%284x%2B3y%29=-3%28-15%29 Multiply the both sides of the second equation by -3.


-12x-9y=45 Distribute and multiply.


So we have the new system of equations:
system%2812x%2B14y=-10%2C-12x-9y=45%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:


%2812x%2B14y%29%2B%28-12x-9y%29=%28-10%29%2B%2845%29


%2812x%2B-12x%29%2B%2814y%2B-9y%29=-10%2B45 Group like terms.


0x%2B5y=35 Combine like terms.


5y=35 Simplify.


y=%2835%29%2F%285%29 Divide both sides by 5 to isolate y.


y=7 Reduce.


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12x%2B14y=-10 Now go back to the first equation.


12x%2B14%287%29=-10 Plug in y=7.


12x%2B98=-10 Multiply.


12x=-10-98 Subtract 98 from both sides.


12x=-108 Combine like terms on the right side.


x=%28-108%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=-9 Reduce.


So our answer is x=-9 and y=7.


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 6x%2B7y=-5 (red) and 4x%2B3y=-15 (green)