SOLUTION: Solve the system using substitution. x + 6z = -45 5x + 3y - 2z = -33 y + 4z = -24 I think i keep messing up the first step because when im finished i get x=-9, y=8, z=-6,

Question 827544: Solve the system using substitution.
x + 6z = -45
5x + 3y - 2z = -33
y + 4z = -24
I think i keep messing up the first step because when im finished i get
x=-9, y=8, z=-6, but it doesnt work when pluging it back in
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x + 6z = -45
5x + 3y - 2z = -33
y + 4z = -24
---
copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution by matrix-method:
x = -9
y = 0
z = -6
---
system matrix
1 0 6
5 3 -2
0 1 4
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inverse of system matrix
0.31818182 0.13636364 -0.40909091
-0.45454545 0.090909091 0.72727273
0.11363636 -0.022727273 0.068181818
---
determinant of system matrix = 44
---
now by substitution:
---
x + 6z = -45
x = -6z - 45
---
5x + 3y - 2z = -33
5(-6z - 45) + 3y - 2z = -33
-30z - 225 + 3y - 2z = -33
---
3y - 32z = 192
---
y + 4z = -24
y = -4z - 24
---
3y - 32z = 192
3(-4z - 24) - 32z = 192
-12z - 72 - 32z = 192
-44z = 264
z = -264/44
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z = -6
---
y = -4z - 24
y = -4(-6) - 24
---
y = 0
---
x = -6z - 45
x = -6(-6) - 45
---
x = -9
---
---
solution by substitution-method:
x = -9
y = 0
z = -6
---
the two methods agree.
---
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---
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---
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