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Question 415646: can somebody tell how to figure out how to solve this problum it says to solve by the elimination method but i dont understand what that means help please.
7r-2s=26
2r+7s=15
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! elimination method means you transform one or both of the equation so that when you add or subtract the equations together, one of the unknown variables disappears.
your problem is:
7r-2s=26
2r+7s=15
if you multiply the first equation by 2 and you multiply the second equation by 7, you should be able to eliminate at least one variable.
(7r - 2s = 26) * 2 becomes 14r - 4s = 52
(2r + 7s = 15) * 7 becomes 14r + 49s = 105
your 2 equations are now:
14r - 4s = 52
14r + 49s = 105
now, when you subtract one equation from the other, the unknown variable of r will disappear.
subtract the first equation from the second equation to get:
53s = 52
this is because:
14r-14r = 0
49s - (-4s) = 49s + 4s = 53s
105 - 52 = 53
you can now solve for s to get s = 1
you now go back to your original equations of:
7r-2s=26
2r+7s=15
substitute for s in the first equation to solve for r.
you get:
7r-2s = 26 becomes 7r - 2 = 26
add 2 to both sides of this equation to get 7r = 28
divide both sides of this equation by 7 to get r = 4
you now have s = 1 and r = 4
substitute for both r and s in the second original equation to confirm these numbers are good.
they are only good if they solve both equations simultaneously.
the second equation is 2r+7s=15.
substitute for r and s to get 2*4 + 7*1 = 15.
simplify to get 8 + 7 = 15 which is true.
the values for r and s are good.
the answer is:
r = 4
s = 1
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