Question

Part 1: Explain, in complete sentences, which method you would use to solve the following system of equations.

Part 2: Explain why you chose that method

Part 3: Provide the solution to the system.
x – 2y + z = 0
2x – 3y – 4z = –9
x + 2y – 5z = 0

Answer 1

I would multiply x –2y + z = 0 by -1, then add x –2y + z = 0 to x + 2y – 5z = 0

(-x + 2y - z = 0)+(x + 2y -5z = 0)
4y -6z = 0

Next, multiply x + 2y - 5z = 0 by -2 and add that to 2x - 3y - 4z = -9

(-2x - 4y + 10z = 0)+(2x - 3y - 4z = -9)
-7y + 6z = -9

Let's add these two equations.

(-7y + 6z = -9)+(4y -6z = 0)

-3y = -9
y = 3

So, now we have a y-value. Let's plug it into our 3 original equations.

x – 2y + z = 0
2x – 3y – 4z = –9
x + 2y – 5z = 0

x - 2(3) + z = 0
2x - 3(3) - 4z = -9
x + 2(3) - 5z = 0

x + z = 6
2x - 4z = 0
x -5z = -6

Now, let's solve for x in two of the equations.

x = 6-z
x = -6 +5z

Set these equal to each other.

6-z = -6 + 5z
12 = 6z
z = 2

Now that we have a z-value, we can plug in z in these three equations.

x + z = 6
2x - 4z = 0
x -5z = -6

x + (2) = 6
2x - 4(2) = 0
x - 5(2) = -6
x = 4

So, our solution to this system of equations is: (4, 3, 2) assuming (x, y, z)

Answer 2

thanks that is what i got!

Answer 3

:) Good job.

Answer 4

check out the one i just posted PLEASE! :(