The sum of two numbers is 18. Twice the first number plus three times the second number equals 40. Find the numbers.

a+b=18

2a+3b=40

Here's two solutions:

A) Multiply the first equation by (-2) & sum then the two equations, resulting ''b''. Or, multiply that first equation by (-3) Summing them you get ''a''. Whatever you obtain, introduce it into an equation and obtain the other one.

B) You have a system of two equation with two unknown terms. Get one unknown term (e. g. ''a'') out of the first equation (a=18-b) & introduce it (18-b) into the other equation, the second one, instead of that unknown term, and you'll get this second equation written within just one unknown term (2 (18-b) + 3b=40; 36-2b+3b=40. With the term this way defined, you'll have also the first one.

x+y=18; 2x+3y=40

y=18-x, 2x+3 (18-x) = 40

2x+54-3x=40

-x=-14

x=14

14+y=18, y=4

14+4=18

2 (14) + 3 (4) = 40, 28+12=40