Answer
The solution to this system of equations is $(8, -4, 2)$.
Work Step by Step
Substitute $2$ in for $z$ in the second equation to solve for $y$:
$y + 2(2) = 0$
$y + 4 = 0$
$y = -4$
We now have the values for $y$ and $z$, so let's plug these values into the first equation to find $x$:
$x + 2(-4) + 3(2) = 6$
$x - 8 + 6 = 6$
$x - 2 = 6$
$x = 8$
The solution to this system of equations is $(8, -4, 2)$.
To check if our solution is correct, we plug all three variables into one of the equations and see if the left and right sides equal one another. Let's use the first equation:
$8 + 2(-4) + 3(2) = 6$
$8 - 8 + 6 = 6$
$0 + 6 = 6$
$6 = 6$
The left and right sides are equal; therefore, this solution is correct.
