Can you manipulate the coefficients of any variable terms such that they could be eliminated?
(0,3,4)
Practice makes perfect
The given system consists of equations of planes. Notice that the coefficient of z in the first equation is the additive inverse of the coefficient of z in the second equation; they will add to be 0. Let's use the Elimination Method to find a solution to this system.
2x+3y - 2z=1 & (I) - x-y + 2z=5 & (II) 3x+2y-3z=-6 & (III)
We can start by adding the second equation to the first equation to eliminate the z-terms.
2x+3y-2z=1 & (I) - x-y+2z=5 & (II) 3x+2y-3z=-6 & (III)
Having eliminated the z-variable from the first equation, we can continue by creating additive inverse coefficients for z in the second and third equations. Then, we can add or subtract these equations to eliminate z from the second equation.
Next, we will use our two equations that are only in terms of x and y 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.
