the greater of two numbers is 1 more than twice smaller. three times greater exceeds 5 times the smaller by 10. find the three numbers.

The value of the greater number is 15. The value of the smaller number is 7.

x = 2y + 1

3x = 5y + 10

Because we have a value for x we can plug this value in to find the value of y.

3 (2y + 1) = 5y + 10

Distributive property.

6y + 3 = 5y + 10

Subtract 5y from both sides.

y + 3 = 10

Subtract 3 from both sides.

y = 7

We can plug this value back into the original equation to find the value of x.

x = 2 (7) + 1

x = 15