SOLUTION: If 5 times the first number plus three times the second number equals 47, and 10 times the first number minus 4 times the second number equals 54, what are the numbers?

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Question 236513: If 5 times the first number plus three times the second number equals 47, and 10 times the first number minus 4 times the second number equals 54, what are the numbers?
Answer by Anthea Lawn(22) About Me  (Show Source):
You can put this solution on YOUR website!
okay, call the first number x and the second number y
5x + 3y = 47
10x -4y = 54
So now we have two simultaneous equations. Double everything in the top equation :
10x + 6y = 94
Now both equations start with a 10x So take the second equation away from the new top one and the 10x bits will disappear :
(10x - 10x) + 6y - (-4y) = 94 - 54
10y = 40 (because taking away a minus equals a plus)
y = 4
Substituting back into either of the original equations gives x = 7
So the two numbers are 7 and 4.