Question

What is the solution to this system of equations?

Answer 1

Since this is multiple choice ...

• check if B is correct:

x = 0, y = 4, z = 1   ⇒   3x - y + 4z = -4 + 4 = 0 ≠ -10

(it's not)

• check if C is correct:

x = -2, y = 4, z = 0

⇒   3x - y + 4z = -6 - 4 + 0 = -10

⇒   3x - y + 4z = 2 + 4 + 0 = 6

⇒   3x - y + 4z = -4 - 4 + 0 = -8

While this solution does satisfy the system, it can still have infinitely many other solutions that would work.

• check if D is correct:

Eliminate one of the variables from each equation. For instance,

(3x - y + 4z) + (-x + y + 2z) = -10 + 6

2x + 6z = -4

x + 3z = -2

and

(2x - y + z) + (-x + y + 2z) = -8 + 6

x + 3z = -2

but now it's impossible to eliminate one of the variables.

Therefore there are infinitely many solutions to the system [D].