The given system consists of equations of planes. Notice that the coefficients of y in the first and the third equations are the additive inverse of the coefficient of y in the second equation; they will add to be 0. Let's use the Elimination Method to find a solution to this system.
x - y+z=-1 & (I) x + y+3z=-3 & (II) 2x - y+2z=0 & (III)
We can start by adding the second equation to the first and the third equations to eliminate the y-terms.
Next, we will use our two equations that are only in terms of x 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.
The solution to the system is ( 4, 2, -3). This is the singular point at which all three planes intersect.
Now we can check our solution by substituting the values into the system.
