Question

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?

Answer 1

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

Explanation:

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`.