Sum of three numbers is 17:
a + b + c = 17
First is 2 greater than two times the third:
a = 2c + 2
Sum of second and third is 9:
b + c = 9
First find the variables in terms of their relationship with other variables. We have variable a because we know that a = 2c + 2. We also know variable b because we have that b + c = 9, so b = 9 - c. We also know variable c because we have that b + c = 9, so c = 9 - b.
Now plug in the equations instead of their variables into the first equation so at the end we would only have one variable, which is easy to figure out.
First get rid of a by putting (2c + 2) instead of it. So the equation would be:
(2c + 2) + b + c = 17.
Then get rid of b by putting (9 - c) instead of it. So the equation would now be:
(2c + 2) + (9 - c) + c = 17.
To simplify this and figure out c, combine like terms so the equation would be:
2c + 11 = 17
Then get c by itself by subtracting 11 from both sides and then dividing both sides by 2 so the equation would be:
c = 3
Once you have c, you can figure out the other numbers by plugging it in:
for example, because a = 2c + 2, just plug in 3 for c to get a = 2(3) + 2, which is 6 + 2, which is 8, so a = 8.
also, because b = 9 - c, just plug in 3 for c to get b = 9 - 3, which is 6, so b = 6.
And since 8 + 6 + 3 = 17, and 8 is 2 greater than 2 x 3, and 6 + 3 = 9, those are the three numbers.