Question

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)

Answer 1

a = 6/5

b = 7/8

c = 1/5

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.