SOLUTION: I can not determine the answer to: 13x-3y=-50 { 12x+5y=16 in either the substitution method or the elimination method..

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Question 183398: I can not determine the answer to:
13x-3y=-50
{
12x+5y=16
in either the substitution method or the elimination method..
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to use elimination to solve this system:


13x-3y=-50+ Start with the first equation


5%2813x-3y%29=5%28-50%29+ Multiply both sides by 5


65x-15y=-250+ Distribute and multiply.

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12x%2B5y=16 Move onto the second equation


3%2812x%2B5y%29=3%2816%29 Multiply both sides by 3


36x%2B15y=48 Distribute and multiply.


So we have the new system of equations:
system%2865x-15y=-250%2C36x%2B15y=48%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:


%2865x-15y%29%2B%2836x%2B15y%29=%28-250%29%2B%2848%29


%2865x%2B36x%29%2B%28-15y%2B15y%29=-250%2B48 Group like terms.


101x%2B0y=-202 Combine like terms. Notice how the y terms cancel out.


101x=-202 Simplify.


x=%28-202%29%2F%28101%29 Divide both sides by 101 to isolate x.


x=-2 Reduce.


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65x-15y=-250 Now go back to the first equation.


65%28-2%29-15y=-250 Plug in x=-2.


-130-15y=-250 Multiply.


-15y=-250%2B130 Add 130 to both sides.


-15y=-120 Combine like terms on the right side.


y=%28-120%29%2F%28-15%29 Divide both sides by -15 to isolate y.


y=8 Reduce.


So our answer is x=-2 and y=8.


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 13x-3y=-50 (red) and 12x%2B5y=16 (green)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Multiply (1) by 5 and (2) by 3:




Add the two equations:



Solve for x, then substitute the value found for x into either (1) or (2) to solve for y.



John