SOLUTION: i need step by step solution using elimination method,thank u 3x+4y=-15 3x+6y=-21

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Question 148096This question is from textbook
: i need step by step solution using elimination method,thank u
3x+4y=-15
3x+6y=-21 This question is from textbook

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%283x%2B4y=-15%2C3x%2B6y=-21%29


-1%283x%2B6y%29=-1%28-21%29 Multiply the both sides of the second equation by -1.


-3x-6y=21 Distribute and multiply.


So we have the new system of equations:
system%283x%2B4y=-15%2C-3x-6y=21%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:


%283x%2B4y%29%2B%28-3x-6y%29=%28-15%29%2B%2821%29


%283x%2B-3x%29%2B%284y%2B-6y%29=-15%2B21 Group like terms.


0x%2B-2y=6 Combine like terms. Notice how the x terms cancel out.


-2y=6 Simplify.


y=%286%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-3 Reduce.


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


3x%2B4y=-15 Now go back to the first equation.


3x%2B4%28-3%29=-15 Plug in y=-3.


3x-12=-15 Multiply.


3x=-15%2B12 Add 12 to both sides.


3x=-3 Combine like terms on the right side.


x=%28-3%29%2F%283%29 Divide both sides by 3 to isolate x.


x=-1 Reduce.


So our answer is x=-1 and y=-3.


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 3x%2B4y=-15 (red) and 3x%2B6y=-21 (green)