SOLUTION: solve by elimination method 7r-2s=31 2r+7s=77

Question 280644: solve by elimination method
7r-2s=31
2r+7s=77
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Solving simultaneous equations by the elimination method means to align the equations and add or subtract them to find one value. Then substitute this value to find the other. And so forth.
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7r - 2s = 31
2r + 7s = 77
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The least common multiple of 2 and 7 is 14,
so multiply the first equation by 7 and the second by 2
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7(7r +2s) = 7(31)
49r - 14s = 217
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2(2r +7s) = 2(77)
4r +14s = 154
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So now we have two new equations...
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49r - 14s = 217
4r + 14s = 154
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adding
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53r = 371
r = 7
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substituting into one of the equations, we can find 's'
7r -2s = 31
7(7) -2s = 31
-2s = 31 - 49
-2s = -18
s = 9
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check by substituting in the second equation
2r + 7s = 77 ??
2r = 2*7 = 14
7s = 7*9 = 63
14 + 63 = 77
Yes!
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Answer:
r = 7
s = 9
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Done.
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