a2 - b2 = -24 - In this equation, a and b are constants. If a - b = -8, what is the value of b?

Question

a² - b² = -24

 

In the equation above, a and b are constants. If a - b = -8, what is the value of b?

Answer 1

Hello, T,

   You have a system of equations.  Here are some steps: 

1.   Use the second equation and solve for "a":     a—b=-8    Add "b" to both sides of equal sign.    a=b—8.

 

2.  Take the a²-b²=-24 and substitute "a=b—8" into the (a² )      (b-8)²— (b)² = -24

Note:  (b-8)² = (b-8)(b-8)                                          b² —16b +64—b² = -24   Solve for "b."

                                                                                –16b +64  = -24  

 

 

Simplify by getting letters on one side and numbers on the other.  In other words, solve for "b."  Then simplify your answer, and you're done.

 

If you want to check the answer, just substitute "b" into the second equation, and you can solve for "a."  Finally, for the check, substitutes the values for "a" and "b" into the first equation.  If your "b" answer was correct, you should get  -24=-24.  

I hope that these steps help.                    Susan C.