Can you manipulate the coefficients of any variable terms such that they could be eliminated?
(2,0,- 2)
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 third equation; they will add to be 0. Let's use the Elimination Method to find a solution to this system.
7x-2y-5z=24 & (I) - x+3y+4z=- 10 & (II) x-y-z=4 & (III)
⇓
7x-2y-5z=24 & (I) - 1x+3y+4z=- 10 & (II) 1x-y-z=4 & (III)
We can start by adding the third equation to the second equation to eliminate the x-terms.
Having eliminated the x-variable from the second equation, we can continue by creating additive inverse coefficients for x in the first and third equations. Then we can add or subtract these equations to eliminate x from the second equation.
Next, we use our two equations that are only in terms of y 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.
The solution to the system is ( 2, 0, - 2). This is the singular point at which all three planes intersect. Now we can check our solution by substituting the values into the system.
