Question

Solve the system. If there's no unique solution, label the system as either dependent or inconsistent.

Answer 1

Answer:

simplify bottom equation by dividing all terms by 4 to get -x + y - 4z = -5.

divide all terms by -1 to get x - y + 4z = 5.

now you’re only left with two equations since the bottom two are essentially the same.

solve for x in the second equation.

x = 5 + y - 4z

substitute x into the first equation and simplify.

2 (5 + y - 4z) + y + 3z = 12

10 + 2y - 8z + y + 3z = 12

3y - 5z = 2

substitute x into the second equation and solve for y.

5 + y - 4z - y

Answer 2

Simplify bottom equation by dividing all terms by 4 to get -x + y - 4z = -5.

divide all terms by -1 to get x - y + 4z = 5.

now you’re only left with two equations since the bottom two are essentially the same.

solve for x in the second equation.
x = 5 + y - 4z

substitute x into the first equation and simplify.
2 (5 + y - 4z) + y + 3z = 12
10 + 2y - 8z + y + 3z = 12
3y - 5z = 2

substitute x into the second equation and solve for y.
5 + y - 4z - y + 4z = 5

everything cancels each other out! this means that this is an inconsistent system. there is no solution. :(