Posted by **Sue** on Monday, November 26, 2012 at 1:46pm.

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?

please explain the steps

- algebra -
**Steve**, Monday, November 26, 2012 at 2:35pm
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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