# 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?

##### 1 Answer

Nov 17, 2016

The two numbers are:

#### Explanation:

If we call the first number

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

Multiply both of these equations by

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

Then subtracting to eliminate

#{: ("(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