12x+4y+2z=-7 (1)

3x-12y+6z=-4 (2)
9x-16y+4z=-3 (3)
solve the system.
show steps and answers i tried this problem really difficult

And exactly what didn't you like about the answer I gave you a few minutes ago to this question?

thank you.

you are welcome, let me know what answers you got

To solve this system of equations, we will use the method of elimination, which involves manipulating the equations to eliminate one of the variables.

Step 1: Pick two equations and eliminate one variable.
Let's eliminate the x-variable from equations (1) and (2). Multiply equation (2) by 4 and equation (1) by 3 to match the coefficients of x:

(3) 12x + 4y + 2z = -7 [multiply by 3]
(4) 12x - 48y + 24z = -16 [multiply by 4]

Now, subtract equation (4) from equation (3):
(3) - (4) = (12x + 4y + 2z) - (12x - 48y + 24z) = -7 - (-16)

This simplifies to:
52y - 22z = -7 + 16
52y - 22z = 9 [equation (5)]

Step 2: Pick two equations and eliminate another variable.
Let's eliminate the y-variable from equations (2) and (3). Multiply equation (2) by 16 and equation (3) by 12 to match the coefficients of y:

(2) 3x - 12y + 6z = -4 [multiply by 16]
(3) 9x - 16y + 4z = -3 [multiply by 12]

Now, subtract equation (3) from equation (2):
(2) - (3) = (3x - 12y + 6z) - (9x - 16y + 4z) = -4 - (-3)

This simplifies to:
x + 10y + 2z = -4 + 3
x + 10y + 2z = -1 [equation (6)]

Step 3: Now, we have two equations with two variables:
Equation (5): 52y - 22z = 9
Equation (6): x + 10y + 2z = -1

From equation (6), we can solve for x:
x = -1 - 10y - 2z [equation (7)]

Step 4: Substitute the value of x from equation (7) into equation (5):
52y - 22z = 9
-1 - 10y - 2z + 10y + 2z = 9 [substituted x]

Simplifying further:
-1 + 9 = 52y - 22z
8 = 52y - 22z [equation (8)]

Step 5: Now, we have two equations with two variables:
Equation (8): 8 = 52y - 22z
Equation (5): 52y - 22z = 9

Since both equations have the same terms, we can conclude that these equations represent the same line. Therefore, the system of equations has no solution.

In conclusion, the given system of equations has no solution.