Question

What is the solution to the system of equations?

x+y+3z=-4
2x-z=-3
-x-y-2z=5

a. (-1, -6, 1)
b. (1, -6, 1)
c. (-1, 6, 1)
d. (-1, -6, -1)

Answer 1

a

Explanation:

Let's use the elimination method on equations 1 and 3 and see what happens:

x + y + 3z = -4

-x - y - 2z = 5

It looks like both the x terms and the y terms cancel out leaving us with the fact that z = 1.

Let's go back to the second equation now and sub in a 1 for z:

2x - z = -3 implies 2x - 1 = -3 and x = -1.

Pick any equation now to sub in the known values to find y. I chose the first one, just because:

x + y + 3z = -4 implies -1 + y + 3(1) = -4 and

-1 + y + 3 = -4 so

y + 2 = -4 and

y = -6

So the solution set is (-1, -6, 1)