Can you manipulate the coefficients of any variable terms such that they could be eliminated?
(2,1,-5)
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-y + z=-2 & (I) x+3y - z=10 & (II) x+2z=-8 & (III)
We can start by adding the second equation to the first equation to eliminate the z-terms.
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.
