I need step by step on how to solve this problem plz help I've been trying to figure it out for like an hour. Solve the system using the elimination method.

4x-y+2z=-18
-x+2y+z=11
3x+3y-4z=44

There is a nice elimination calculator online. It will show you all the details.

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

Step 1: Choose two equations and eliminate one variable.

Let's eliminate the variable "x" from the first and second equations.

To do this, multiply both sides of the second equation by 4 to make the coefficient of "x" in both equations the same (4 in this case).

Original equations:
4x - y + 2z = -18 (Equation 1)
-x + 2y + z = 11 (Equation 2)

Multiply Equation 2 by 4:
-4x + 8y + 4z = 44 (Equation 3)

Step 2: Add the equations together to eliminate "x".
Now, add Equation 1 and Equation 3 together:

(Equation 1) + (Equation 3):
4x - y + 2z + (-4x + 8y + 4z) = -18 + 44

This simplifies to:
7y + 6z = 26 (Equation 4)

Step 3: Choose two different equations and eliminate the same variable as Step 1.
Next, let's eliminate the variable "y" from Equations 3 and 4.
Multiply Equation 4 by 2 to make the coefficient of "y" in both equations the same (14 in this case).

Original Equation 3:
-4x + 8y + 4z = 44 (Equation 3)

Multiply Equation 4 by 2:
14y + 12z = 52 (Equation 5)

Step 4: Add the equations together to eliminate "y".
Now, add Equation 3 and Equation 5 together:

(Equation 3) + (Equation 5):
-4x + 8y + 4z + (14y + 12z) = 44 + 52

This simplifies to:
8z = 96

Step 5: Solve for the remaining variable.
Divide both sides of the equation by 8:

8z/8 = 96/8

This gives us:
z = 12

Step 6: Substitute the value of "z" into one of the equations.
Let's substitute z = 12 into Equation 4:

7y + 6z = 26

Plugging in z = 12:
7y + 6(12) = 26

Simplifying,
7y + 72 = 26

Step 7: Solve for the remaining variable.
Subtract 72 from both sides of the equation:

7y = 26 - 72

This gives us:
7y = -46

Divide both sides of the equation by 7:

7y/7 = -46/7

The solution is:
y = -6.57

Step 8: Substitute the values of "y" and "z" into one of the original equations.
Let's substitute y = -6.57 and z = 12 into Equation 1:

4x - y + 2z = -18

Plugging in the values:
4x - (-6.57) + 2(12) = -18

Simplifying,
4x + 6.57 + 24 = -18

Combine like terms:
4x + 30.57 = -18

Subtract 30.57 from both sides of the equation:
4x = -18 - 30.57

This gives us:
4x = -48.57

Divide both sides of the equation by 4:
4x/4 = -48.57/4

The solution is:
x = -12.14

Therefore, the system of equations has the solution:
x = -12.14, y = -6.57, and z = 12.

To solve the system using the elimination method, follow these step-by-step instructions:

Step 1: Write down the system of equations:
4x - y + 2z = -18 ---(Equation 1)
-x + 2y + z = 11 ---(Equation 2)
3x + 3y - 4z = 44 ---(Equation 3)

Step 2: Choose two equations to eliminate a variable. Let's eliminate the 'y' variable. Multiply Equation 1 by 2 and Equation 2 by -1 to make the coefficients of 'y' opposite:
2(4x - y + 2z) = 2(-18)
-1(-x + 2y + z) = -1(11)

This simplifies to:
8x - 2y + 4z = -36 ---(Equation 4)
x - 2y - z = -11 ---(Equation 5)

Step 3: Add Equation 4 and Equation 5 to eliminate the 'y' variable:
8x - 2y + 4z + (x - 2y - z) = -36 + (-11)

This simplifies to:
9x + 3z = -47 ---(Equation 6)

Step 4: Now, choose another set of equations to eliminate 'y'. Let's eliminate the 'y' variable again. Multiply Equation 2 by 2 and Equation 3 by -2 to make the coefficients of 'y' opposite:
2(-x + 2y + z) = 2(11)
-2(3x + 3y - 4z) = -2(44)

This simplifies to:
-2x + 4y + 2z = 22 ---(Equation 7)
-6x - 6y + 8z = -88 ---(Equation 8)

Step 5: Add Equation 7 and Equation 8 to eliminate the 'y' variable:
-2x + 4y + 2z + (-6x - 6y + 8z) = 22 + (-88)

This simplifies to:
-8x + 10z = -66 ---(Equation 9)

Step 6: Now, we have two equations involving only 'x' and 'z':
9x + 3z = -47 ---(Equation 6)
-8x + 10z = -66 ---(Equation 9)

Step 7: Solve this system of equations. To eliminate 'z', multiply Equation 6 by 10 and Equation 9 by 3:
10(9x + 3z) = 10(-47)
3(-8x + 10z) = 3(-66)

This simplifies to:
90x + 30z = -470 ---(Equation 10)
-24x + 30z = -198 ---(Equation 11)

Step 8: Add Equation 10 and Equation 11 to eliminate 'z':
90x + 30z + (-24x + 30z) = -470 + (-198)

This simplifies to:
66x = -668

Step 9: Solve for 'x' by dividing both sides of the equation by 66:
x = -668 / 66
x = -10

Step 10: Substitute the value of 'x' back into Equation 6 to solve for 'z':
9(-10) + 3z = -47
-90 + 3z = -47
3z = -47 + 90
3z = 43
z = 43 / 3
z = 14.33 (rounded to two decimal places)

Step 11: Substitute the values of 'x' and 'z' into Equation 1 (or any other equation) to solve for 'y':
4(-10) - y + 2(14.33) = -18
-40 - y + 28.66 = -18
-y - 11.34 = -18
-y = -18 + 11.34
-y = -6.66
y = 6.66 (rounded to two decimal places)

Therefore, the solution to the system of equations is:
x = -10
y = 6.66
z = 14.33