SOLUTION: how do i solve these two problams using the elimination method ? 1. 10x+6y =0 -7x+2y =31 for this one i got (9.3, -15.5) but i have a feeling that is wrong and 2.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: how do i solve these two problams using the elimination method ? 1. 10x+6y =0 -7x+2y =31 for this one i got (9.3, -15.5) but i have a feeling that is wrong and 2.       Log On


   

Question 225185: how do i solve these two problams using the elimination method ?
1. 10x+6y =0
-7x+2y =31
for this one i got (9.3, -15.5) but i have a feeling that is wrong
and 2. 3x+4y=-13
5x+6y=-19
for this one i got (-25, 15.5) but again , because the answers i gto are so big and decimals, i think im doing the problems wrong

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



Start with the given system of equations:
system%2810x%2B6y=0%2C-7x%2B2y=31%29


-3%28-7x%2B2y%29=-3%2831%29 Multiply the both sides of the second equation by -3.


21x-6y=-93 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B6y=0%2C21x-6y=-93%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:


%2810x%2B6y%29%2B%2821x-6y%29=%280%29%2B%28-93%29


%2810x%2B21x%29%2B%286y%2B-6y%29=0%2B-93 Group like terms.


31x%2B0y=-93 Combine like terms.


31x=-93 Simplify.


x=%28-93%29%2F%2831%29 Divide both sides by 31 to isolate x.


x=-3 Reduce.


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


10x%2B6y=0 Now go back to the first equation.


10%28-3%29%2B6y=0 Plug in x=-3.


-30%2B6y=0 Multiply.


6y=0%2B30 Add 30 to both sides.


6y=30 Combine like terms on the right side.


y=%2830%29%2F%286%29 Divide both sides by 6 to isolate y.


y=5 Reduce.


So the solutions are x=-3 and y=5.


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 10x%2B6y=0 (red) and -7x%2B2y=31 (green)




# 2




Start with the given system of equations:
system%283x%2B4y=-13%2C5x%2B6y=-19%29


3%283x%2B4y%29=3%28-13%29 Multiply the both sides of the first equation by 3.


9x%2B12y=-39 Distribute and multiply.


-2%285x%2B6y%29=-2%28-19%29 Multiply the both sides of the second equation by -2.


-10x-12y=38 Distribute and multiply.


So we have the new system of equations:
system%289x%2B12y=-39%2C-10x-12y=38%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:


%289x%2B12y%29%2B%28-10x-12y%29=%28-39%29%2B%2838%29


%289x%2B-10x%29%2B%2812y%2B-12y%29=-39%2B38 Group like terms.


-x%2B0y=-1 Combine like terms.


-x=-1 Simplify.


x=%28-1%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=1 Reduce.


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


9x%2B12y=-39 Now go back to the first equation.


9%281%29%2B12y=-39 Plug in x=1.


9%2B12y=-39 Multiply.


12y=-39-9 Subtract 9 from both sides.


12y=-48 Combine like terms on the right side.


y=%28-48%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=-4 Reduce.


So the solutions are x=1 and y=-4.


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=-13 (red) and 5x%2B6y=-19 (green)