Question

If 5b=6a+16 and 9a=7b-20, then what are the values of a and b? show work.

Answer 1

Answer:

a = 4, b = 8

Step-by-step explanation:

Rewrite 5b=6a+16 and 9a=7b-20 vertically:

5b=6a+16

9a=7b-20

Let's use substitution.  Solve the first equation for b:

       6a + 16

b = --------------

             5

Substitute this result into the second equation:

9a = 7(b) + 16, or

             6a + 16

9a = 7*-------------- - 20

                   5

Eliminate the fraction by multiplying all three terms by 5:

45a = 7(6a + 16) - 100, or

3a =        112 - 100, or:

3a = 12, which leads to a = 4.  

Find b by subbing 4 for a in either of the given equations:

5b = 6(4) + 16, or

5b = 40, leading to b = 8

The solution is a = 4, b = 8