The given system consists of equations of planes. Notice that the coefficient of c in the first equation is the additive inverse of the coefficient of c in the second equation; they will add to be 0. Let's use the Elimination Method to find a solution to this system.
a+b + c=-3 & (I) 3b - c=4 & (II) 2a-b-2c=-5 & (III)
We can start by adding the first equation to the second equation to eliminate the c-terms.
Having eliminated the c-variable from the second equation, we can continue by creating additive inverse coefficients for c in the first and second equations. Then, we can add or subtract these equations to eliminate c from the third equation.
Next, we use our two equations that are only in terms of a and b 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 ( -3, 1, -1). This is the singular point at which all three planes intersect.
Now, we can check our solution by substituting the values into the system.
