Question

select the correct answer.
what is the solution to this system of equations?
$x + y - 2z = 2$
$3x + 3y - 6z = 6$
$-2x - 2y + 4z = -4$
$(2,0,0)$
no solutions
infinite solutions
$(1,1,0)$

Explanation:

Step1: Analyze equation scaling

Notice that Equation 2: $3x + 3y - 6z = 6$ is Equation 1: $x + y - 2z = 2$ multiplied by 3, so they are identical.
Equation 3: $-2x - 2y + 4z = -4$ is Equation 1 multiplied by $-2$, so it is also identical to Equation 1.

Step2: Determine solution type

All three equations represent the same plane. A single plane has infinitely many points (solutions) that satisfy it.

Answer:

infinite solutions