Solving Systems Part 3

Question

x+y-z=2

x-y-2z=2

2x+3y+z=9

Answer 1

Hi Minah.

 

You have 3 equations:

 

1. x + y - z = 2
2. x - y - 2z = 2

3. 2x + 3y + x = 9

 

Your job is to successively eliminate variables by adding equations together. Add equation 1 and equation 2 together to eliminate the y.

 

x + y - z = 2

x - y - 2z = 2

 

2x - 3z = 4

 

Add 3 times equation 2 to equation 3 to eliminate the y again.

 

3x - 3y - 6z = 6

2x + 3y + z = 9

 

5x - 5z = 15

 

You now have two equations with just x and z. Eliminate one of the remaining variables. I'm going to eliminate x.

 

Multiply your first new equation by 5 and multiply your second new equation by -2. Then add them together.

 

10x - 15z = 20

-10x + 10z = -30

 

-5z = -10

 

z = 2

 

Plug this z value into one of your new equations to find x.

 

5x - 5(2) = 15

5x - 10 = 15

5x = 25

 

x = 5

 

Plug your known x and z values into one of your original equations to resolve y.

 

(5) + y - (2) = 2

 

y + 3 = 2

 

y = -1

 

So your system's solution is:

 

(5, -1, 2)

 

Always good to check these answers with your original equations.

 

(5) + (-1) - (2) = 2

 

Check.

 

(5) - (-1) - 2(2) = 2

 

Check.

 

2(5) + 3(-1) + (2) = 9

 

Checkmate.

 

Hope this helps.