Can you help me solve this equation step by step?

Question

-5x – 5y + 2z = 18
-3x + 5y + 1z = -12
2x – 4y + 0z = 6

Answer 1

The third Equation

2x - 4y + 0z = 6

0z = 0

Therefore this problem has no solution

- - - - - - -s-

Answer 2

You can add two equations together to reduce the number of variables:

-5x - 5y + 2z = 18
-3x + 5y + 1z = -12
-------------------------
-8x + 3z = 6

You can also multiply an entire equation by a non-zero number and maintain the equality:

-5x - 5y + 2z = 18
6x -10y - 2z = 24 { Mulitplied by -2 }
-------------------------
x - 15y = 42

Taking this equation and the last one you gave, we have:

2x - 4y = 6
x - 15y = 42

2x - 4y = 6
-2x + 30y = -84 { Multiply by -2 }
------------------------
26y = -78
y = -3

x - 15(-3) = 42
x + 45 = 42
x = -3

Now, taking the second equation you gave, and substituting for x and y, we have:

-3(-3) + 5(-3) + z = -12
9 - 15 + z = -12
z - 6 = -12
z = -6

So, there you have it: x = -3, y = -3 and z = -6. QED

Answer 3

-5x=5y-2z+18

(5y-2z+18)-5y +2z=18

18=18



-3x=-5y-1z-12

(5y-1z-12) +5y +1z =-12

-12=-12




2x=4y +6

(4y +6) -4y = 6

6=6

Answer 4

add first 2 eqns u get
-8x+3z=6
so z=(6+8x)/3
substitute z value in 2nd and 3rd eqn
we get after taking 3 as whole denominator and cross multiplication
-9x+15y+6+8x=-36(2nd)
-x+15y=-42 ---1
2x-4y=6 ( divide by 2)
x-2y=3 ---2

solve above 2 eqns by adding
-x+15y=-42
x-2y=3
=13y=-39
y=-3

substitue in 3rd eqn
2x-4(-3)=6
2x-12=6
2x=18
x=9

substitute x and y values in 2nd eqn
-3(9)+5(-3)+z=-12
-27-15+z=-12
-42+z=-12
z=-12+42
z=30