Question

When I add my second number to twice my first number, the total is 10. When I add twice my second number to my first number, the total is 11?

Answer 1

Define x and y:
Let the first number be x and the second number be y.

Setup the equations:
y + 2x = 10 ----------- (1)
2y + x = 11  ----------- (2)

Solve x;

From (1):
y + 2x = 10
y = 10 - 2x  ----------- Sub into (2)

2(10 - 2x) + x = 11
20 - 4x + x = 11
20 - 3x = 11
3x = 20 - 11
3x = 9
x = 3  ----------- Sub into (1)

y + 2(3) = 10 
y = 10 - 6
y = 4

Find the numbers:
First number = x = 3
Second number = y = 4

Answer: The two numbers are 3 and 4.