SOLUTION: This is actually solve by elimination problem. 7r - 6s = 22 6r +7s = 31 (this is what I have (32/85,?/85) can you file in the blank for me please? Thank you for your help!

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: This is actually solve by elimination problem. 7r - 6s = 22 6r +7s = 31 (this is what I have (32/85,?/85) can you file in the blank for me please? Thank you for your help!      Log On


   

Question 178302: This is actually solve by elimination problem.
7r - 6s = 22
6r +7s = 31 (this is what I have (32/85,?/85) can you file in the blank for me please? Thank you for your help!
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%287r-6s=22%2C6r%2B7s=31%29


7%287r-6s%29=7%2822%29 Multiply the both sides of the first equation by 7.


49r-42s=154 Distribute and multiply.


6%286r%2B7s%29=6%2831%29 Multiply the both sides of the second equation by 6.


36r%2B42s=186 Distribute and multiply.


So we have the new system of equations:
system%2849r-42s=154%2C36r%2B42s=186%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:


%2849r-42s%29%2B%2836r%2B42s%29=%28154%29%2B%28186%29


%2849r%2B36r%29%2B%28-42s%2B42s%29=154%2B186 Group like terms.


85r%2B0s=340 Combine like terms.


85r=340 Simplify.


r=%28340%29%2F%2885%29 Divide both sides by 85 to isolate r.


r=4 Reduce.


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49r-42s=154 Now go back to the first equation.


49%284%29-42s=154 Plug in r=4.


196-42s=154 Multiply.


-42s=154-196 Subtract 196 from both sides.


-42s=-42 Combine like terms on the right side.


s=%28-42%29%2F%28-42%29 Divide both sides by -42 to isolate s.


s=1 Reduce.


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Answer:


So the solutions are r=4 and s=1 which form the ordered pair


This means that the system is consistent and independent.