Question

A first number plus twice a second number is 10. Twice the first number plus the second totals 26. Find the numbers.

Answer 1

42 and -16

Explanation:

`m,\ n-the\ numbers\\\\\text{The equations:}\\\\(1)\qquad n+2m=10\\(2)\qquad n+m=26\\\\\text{subtract both sides of the equations}\\\\(n+2m)-(n+m)=10-26\\\\n+2m-n-m=-16\qquad\text{combine like terms}\\\\(n-n)+(2m-m)+-16\\\\\boxed{m=-16}\\\\\text{Put the value of m to (2)}:\\\\n+(-16)=26\\\\n-16=26\qquad\text{add 16 to both sides}\\\\\boxed{n=42}`