Exercise 33 Page 172

The given system consists of equations of planes. Notice that the coefficient of $x$ in the first equation is the additive inverse of the coefficient of $x$ in the second equation; they will add to be $0.$ Therefore, let's use the Elimination Method to find a solution to this system. We can start by adding the second equation to the first equation to eliminate the $x\text{-terms}.$ Having eliminated the $x\text{-}$variable from the first equation, we can continue by creating additive inverse coefficients for $x$ in the second and third equations. Then, we can add or subtract these equations to eliminate $x$ from the second equation. Next, we will use our two equations that are only in terms of $y$ and $z$ to solve for the value of one of the variables. We will once again apply the Elimination Method, but this time it will be similar to when using it in a system with only two variables. Now that we know that $y=1,$ we can substitute it into the first equation to find the value of $z.$ The value of $z$ is $3.$ Let's substitute both values into the third equation to find $x.$ The solution to the system is $(8,1,3).$ This is the singular point at which all three planes intersect.