The given system consists of equations of planes. Notice that the coefficient of y in the second equation is the additive inverse of the coefficient of y in the third equation; they will add to be 0. Therefore, let's use the Elimination Method to find a solution to this system.
x+2y+z=4 & (I) 2x - y+4z=-8 & (II) -3x + y-2z=-1 & (III)
We can start by adding the second equation to the third equation to eliminate the y-terms.
x+2y+z=4 & (I) 2x-y+4z=-8 & (II) -3x+y-2z=-1 & (III)
Having eliminated the y-variable from the third equation, we can continue by creating additive inverse coefficients for y in the first and second equations. Then, we can add or subtract these equations to eliminate y from the second equation.
Next, we 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 will be similar to when using it in a system with only two variables.
