The sum of two numbers is 6 . three times the larger number plus three times the smaller number is 36. Find the numbers.

Answer 1

x + y = 6

multiply both sides by 3

3x + 3y =3(6) = 18

"3 times the larger number plus three times the smaller number is 36" is ambiguous. There are two interpretations:

either 1st: 3x +3y = 36

or 2nd: 3(x+3y) = 36

using the 1st interpretation, there is no solution. If you graphed the equations, they'd be parallel lines with no intersection, no solution

if you use the 2nd interpretation, the solution is x=3 and y=3

graphically the two lines would intersect at the point (3,3). That's the "solution" but then x=y and there is no Larger and Smaller number. So. if the solution requires a "Larger" and "Smaller number then there is no solution.