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?

Question

6025 views around the world

You can reuse this answer
Creative Commons License

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 $-1$ .