SOLUTION: i need to know y and x i found x=-3 i cant find y the problem is -4x-3y=3 -2x+5y=21

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Question 299353: i need to know y and x i found x=-3 i cant find y
the problem is
-4x-3y=3
-2x+5y=21
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%28-4x-3y=3%2C-2x%2B5y=21%29


-2%28-2x%2B5y%29=-2%2821%29 Multiply the both sides of the second equation by -2.


4x-10y=-42 Distribute and multiply.


So we have the new system of equations:
system%28-4x-3y=3%2C4x-10y=-42%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:


%28-4x-3y%29%2B%284x-10y%29=%283%29%2B%28-42%29


%28-4x%2B4x%29%2B%28-3y%2B-10y%29=3%2B-42 Group like terms.


0x%2B-13y=-39 Combine like terms.


-13y=-39 Simplify.


y=%28-39%29%2F%28-13%29 Divide both sides by -13 to isolate y.


y=3 Reduce.


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


-4x-3y=3 Now go back to the first equation.


-4x-3%283%29=3 Plug in y=3.


-4x-9=3 Multiply.


-4x=3%2B9 Add 9 to both sides.


-4x=12 Combine like terms on the right side.


x=%2812%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=-3 Reduce.


So the solutions are x=-3 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 -4x-3y=3 (red) and -2x%2B5y=21 (green)