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+1
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5
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i need help with solve the system

 

 Oct 6, 2020
 #1
avatar+1328 
0

Oh man, that's a long problem to solve.

 Oct 6, 2020
 #2
avatar
+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

 Oct 6, 2020
 #3
avatar+1328 
0

Told you it was a long problem 

SmartMathMan  Oct 6, 2020
 #4
avatar+1328 
+1

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

SmartMathMan  Oct 6, 2020
 #5
avatar+27774 
+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 

 Oct 7, 2020

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