Solving a system of equations in three variables

[pleasehelp!]

The problem reads: "The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?"

So I have these two equations:

a + b + c = 24
-2a + 3b - c = 2

It seems like I need a system of three equations to solve this, but the only other one I can come up with is
a² + b² -c² = 0 which I'm having trouble making any use out of. How do I find the lengths of the three sides?

 

[Deleted member 4993]

The problem reads: "The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?"

So I have these two equations:

a + b + c = 24
-2a + 3b - c = 2

It seems like I need a system of three equations to solve this, but the only other one I can come up with is
a² + b² -c² = 0 which I'm having trouble making any use out of. How do I find the lengths of the three sides?

(-2a + 3b - c) + 2(a + b + c) = 50

5b + c = 50 → c = 50 - 5b

Again

(-2a + 3b - c) + (a + b + c) = 26

-a + 4b = 26 → a = 4b - 26

Now use a² + b² = c² and finish it....

 

[pleasehelp!]

awesome, thanks