solve the system by elimination.
6x-6y-4z=-10
-5z+4y-z=-12
2x+3y-2z=9
Multiply the last equation (both sides) by 2. That gives you
4x + 6y - 4z = 18
Add that to
6x - 6y - 4z = -10
That gives you
10x -8z = 8
So far, we have eliminated the variable y.
Use similar tricks to get rid of x or z.
I believe your second equation is typed incorrectly. Did you mean
-5x +4y -z = -12?
To solve the system of equations by elimination, we want to eliminate one variable and solve the resulting system of equations. Let's start by eliminating the variable "z":
1) Multiply the second equation by -1 to make the coefficient of "z" positive:
-5z + 4y - z = -12
-Multiply each term by -1:
5z - 4y + z = 12
2) Add the modified second equation to the first equation:
(6x - 6y - 4z) + (5z - 4y + z) = -10 + 12
Combine like terms:
6x - 6y + 5z - 4y + z = 2
3) Simplify the equation:
6x - 10y + 6z = 2
Now, let's eliminate the variable "y":
4) Multiply the third equation by -2 to make the coefficient of "y" equal to -10:
2x + 3y - 2z = 9
-Multiply each term by -2:
-4x - 6y + 4z = -18
5) Add the modified third equation to the equation we obtained in step 3:
(6x - 10y + 6z) + (-4x - 6y + 4z) = 2 + (-18)
Combine like terms:
2x - 16y + 10z = -16
Now we have the following simplified equation:
2x - 16y + 10z = -16
We have successfully eliminated the variables "y" and "z". To solve for "x", we will use this equation and the previous one.
6) Solve for "x" by isolating it in either of the equations:
2x = 16y - 10z - 16
Divide by 2:
x = 8y - 5z - 8
Now, we have expressions for "x" in terms of "y" and "z". We can substitute these expressions into any of the original equations to solve for the variables.
Note: The solution to this system of equations is not a single set of values for x, y, and z since it is given in terms of other variables.