Solve the following system of equations.

5a - 24b=-15

10a + 45c = 21

48b + 35c = 49

Answer choices

1. There is no solution

2. There are infinitely many solutions.

3. The solution is

(Type an ordered triple, using integers or fractions)

a = 6/5

b = 7/8

c = 1/5

Step-by-step explanation:

We want to make two of these equations be in terms of the same variable, so let's solve the first and third in terms of b.

5a-24b=-15 - > - 3 + 24b/5 = a

48b+35c = 49 - > 49/35 - 48b/35 = 7/5 - 48b/35 = c

Now we can replace the a and c in the second equation and solve for b.

10a+45c=21

10 (-3+24b/5) + 45 (7/5 - 48b/35) = 21

-30 + 48b + 63 - 432b/7 = 21 - > - 12 = - 96b/7 - > b=7/8

Now we can plug b back into the other two to solve for a and c. I will leave that to you unless you would like the steps there.