Will give what is the solution to the system of equations? 2x+y−z=−3 5x−2y+2z=24 3x−z=5 (2, −6, 1) (−5, 4, −3) (−1, 0, −8) (4, 1, 8)

(2,-6,1)

There are a few way to solve this with linear programming, but I am using a simple substitution method.

The goal is to isolate the variables by subtracting or adding the equations. (note: I will refer to the equations as A,B, and C)

2x+y−z=−3

5x−2y+2z=24

3x−z=5

C already has just two variables, x and z. This means a good place to start is by eliminating at least y from one other equation, if not y and another value. To do this, we need to either add two equations where the y values are opposite or subtract one where the y value is equal. However, the two equations with a y value do not have opposite or the same y values.

To get a new equation, we can multiply A by 2. This will give us +2y, which can be added to B to eliminate the value all together- AND the z value. Remember that the WHOLE A equation needs to be multiplied by 2:

2(2x+y-z)=2(-3)

4x+2y-2z=-6

We can now add 2A to B.

(4x+2y-2z=-6)+(5x−2y+2z=24 )

9x=18

x=2

We now know x=2. We can plug this into C to find the z value.

3x−z=5

3(2)-z=5

6-z=5

-z=-1

z=1

With both x and z, we can find y using A.

2x+y−z=−3

2(2)+y-(1)=-3

4+y-1=-3

3+y=-3

y=-6

x=2, y=-6, z=1

true !

step-by-step explanation: