SOLUTION: 7x+6y=30 9x-8y=15 I need to find x & y using Elimination. Thank You~

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Question 529790: 7x+6y=30
9x-8y=15
I need to find x & y using Elimination.
Thank You~
Found 2 solutions by jim_thompson5910, josmiceli:
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%287x%2B6y=30%2C9x-8y=15%29


8%287x%2B6y%29=8%2830%29 Multiply the both sides of the first equation by 8.


56x%2B48y=240 Distribute and multiply.


6%289x-8y%29=6%2815%29 Multiply the both sides of the second equation by 6.


54x-48y=90 Distribute and multiply.


So we have the new system of equations:
system%2856x%2B48y=240%2C54x-48y=90%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:


%2856x%2B48y%29%2B%2854x-48y%29=%28240%29%2B%2890%29


%2856x%2B54x%29%2B%2848y%2B-48y%29=240%2B90 Group like terms.


110x%2B0y=330 Combine like terms.


110x=330 Simplify.


x=%28330%29%2F%28110%29 Divide both sides by 110 to isolate x.


x=3 Reduce.


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56x%2B48y=240 Now go back to the first equation.


56%283%29%2B48y=240 Plug in x=3.


168%2B48y=240 Multiply.


48y=240-168 Subtract 168 from both sides.


48y=72 Combine like terms on the right side.


y=%2872%29%2F%2848%29 Divide both sides by 48 to isolate y.


y=3%2F2 Reduce.


So the solutions are x=3 and y=3%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +7x+%2B+6y+=+30+
(2) +9x+-+8y+=+15+
Multiply both sides of (1) by
4. Multiply both sides of (2) by
3. Then add (1) and (2).
(1) +28x+%2B+24y+=+120+
(2) +27x+-+24y+=+45+
+55x+=+165+
+x+=+3+
Plug this back into (1) or (2)
(2) +9%2A3+-+8y=15+
(2) +27+-+8y+=+15+
(2) +8y+=+27+-+15+
(2) +8y+=+12+
(2) +y+=+3%2F2+
(3,3/2) answer