A first number plus twice a second number is 6. Twice the first number plus the second totals 15 How do you find the numbers?

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Answer 1 · 2016-11-17T20:40:49

The two numbers are: #8# and #-1#.

If we call the first number #x# and the second #y#, then we are given:

#{: ("(i): " x+2y = 6), ("(ii): " 2x+y = 15) :}#

Multiply both of these equations by #2# to get:

#{: ("(iii): " 2x+4y = 12), ("(iv): " 4x+2y = 30) :}#

Then subtracting to eliminate #x# or #y#:

#{: ("(iv) - (i): " 3x = 24 color(white)(--) " Hence: " x = 24/3 = 8), ("(iii) - (ii): " 3y = -3 color(white)(-) " Hence: " y = (-3)/3 = -1) :}#

So the two numbers are #8# and #-1#.