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
Oct 16, 2016

Answer:

#(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):}#