algebra

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if 5 times the first number plus 3 times the second number equals 47 and 10 times the first number minus 4 times the second number equals 54, what are the numbers?

• algebra -

5x + 3y = 47
10x - 4y = 54

substitution:
5x = 47 - 3y, so 10x = 94-6y, thus

10x-4y = 94-6y - 4y = 54
-10y = -40
y=4
so, x = 7

elimination:
multiply the first equation by 4 and the 2nd by 3

20x+12y = 188
30x-12y = 162
add them, and the y's go away:
50x = 350
x=7
so, y=4

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