#2**+1 **

Solve the following system:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 z + 2 x = 4

In the first equation, look to solve for x:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 z + 2 x = 4

Add z + y to both sides:

{-x = z + y - 8

-4 x + 4 y + 5 z = 7

2 z + 2 x = 4

Multiply both sides by - 1

{x = -z - y + 8

-4 x + 4 y + 5 z = 7

2 z + 2 x = 4

Substitute x = -z - y + 8 into the second and third equations:

{x = -z - y + 8

4 y - 4 (-z - y + 8) + 5 z = 7

2 (-z - y + 8) + 2 z = 4

4 y - 4 (-z - y + 8) + 5 z = 4 y + (4 z + 4 y - 32) + 5 z = 9 z + 8 y - 32:

{x = -z - y + 8

9 z + 8 y - 32 = 7

2 (-z - y + 8) + 2 z = 4

2 (-z - y + 8) + 2 z = (-2 z - 2 y + 16) + 2 z = 16 - 2 y:

{x = -z - y + 8

9 z + 8 y - 32 = 7

16 - 2 y = 4

In the third equation, look to solve for y:

{x = -z - y + 8

9 z + 8 y - 32 = 7

16 - 2 y = 4

Subtract 16 from both sides:

{x = -z - y + 8

9 z + 8 y - 32 = 7

-2 y = -12

Divide both sides by -2:

{x = -z - y + 8

9 z + 8 y - 32 = 7

y = 6

Substitute y = 6 into the second equation:

{x = -z - y + 8

9 z + 16 = 7

y = 6

In the second equation, look to solve for z:

{x = -z - y + 8

9 z + 16 = 7

y = 6

Subtract 16 from both sides:

{x = -z - y + 8

9 z = -9

y = 6

Divide both sides by 9:

{x = -z - y + 8

z = -1

y = 6

Substitute z = -1 into the first equation:

{x = 9 - y

z = -1

y = 6

Substitute y = 6 into the first equation:

{x = 3

z = -1

y = 6

Collect results:

**x = 3, y = 6, z = -1**

Guest Oct 6, 2020

#4**+1 **

You should thank the guest for taking the time to solve this crazy thing for you.

SmartMathMan
Oct 6, 2020

#5**+1 **

Multiply equation 1 by 2

-2z-2y-2z = -16 add to equation 3

-2y = -12 y = 6

sub this into equation 2

-4x+5z = -17 and multiply equation 3 by 2

4x +4z = 8 add these equations

9z = -9 z = -1

sub in this result to equation 3

2x + 2(-1) = 4

x = 3

ElectricPavlov Oct 7, 2020