How do I solve this system of equations?

9a + 7b = -30
8b + 5c = 11
-3a + 10c = 73

I've never seen a system of equations when more than one variable is missing in each equation.

1 Answer
sente
Oct 16, 2016

(a, b, c) = (-1, -3, 7)

Explanation:

We can solve a system of equations with missing variables the same way we would one in which each equation contained all variables. It is as if the variables are there and have a coefficient of 0. For this example, let's use elimination.

Multiplying the third equation by 3, we get

-9a+30c = 219

Adding this to the first equation, we get

7b + 30c = 189" "(*)

Multiplying the second equation by 6, we get

48b + 30c = 66

Subtracting this from (*), we get

-41b = 123

=>b = -123/41 = -3

Substituting b=-3 into the second equation, we get

-24+5c = 11

=> c = 7

Substituting b = -3 into the first equation, we get

9a - 21 = -30

=> a = -1

Finally, we check our newfound values a=-1 and c=7 in the third equation to make sure our solution works:

-3(-1) + 10(7) = 3+70 = 73

Thus, we get the solution {(a = -1), (b = -3), (c = 7):}

Related questions
See all questions in Linear Systems with Multiplication
Impact of this question
3152 views around the world
You can reuse this answer
Creative Commons License