SOLUTION: 3x=5-4z X+y+z=5 Y=2z

Algebra ->  Matrices-and-determiminant -> SOLUTION: 3x=5-4z X+y+z=5 Y=2z      Log On


   



Question 925711: 3x=5-4z
X+y+z=5
Y=2z

Found 2 solutions by Fombitz, TimothyLamb:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2B4z=5
x%2By%2Bz=5
y-2z=0
.
.
.
A=%28matrix%283%2C3%2C%0D%0A3%2C0%2C4%2C%0D%0A1%2C1%2C1%2C%0D%0A0%2C1%2C-2%29%29
abs%28A%29=-5
.
.
.
A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A5%2C0%2C4%2C%0D%0A5%2C1%2C1%2C%0D%0A0%2C1%2C-2%29%29
abs%28A%5Bx%5D%29=5
.
.
.
A%5By%5D=%28matrix%283%2C3%2C%0D%0A3%2C5%2C-4%2C%0D%0A1%2C5%2C1%2C%0D%0A0%2C0%2C-2%29%29
abs%28A%5By%5D%29=-20
.
.
.
A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A3%2C0%2C5%2C%0D%0A1%2C1%2C5%2C%0D%0A0%2C1%2C0%29%29
abs%28A%5Bz%5D%29=-10
.
.
.
x=abs%28A%5Bx%5D%29%2Fabs%28A%29=5%2F%28-5%29=-1
.
.
y=abs%28A%5By%5D%29%2Fabs%28A%29=-20%2F%28-5%29=4
.
.
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=-10%2F%28-5%29=2
.
.

Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
3x=5-4z
x+y+z=5
y=2z
---
put the system of linear equations into standard form
---
3x + 4z = 5
x + y + z = 5
y - 2z = 0
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = -1
y = 4
z = 2
---
system matrix
3 0 4
1 1 1
0 1 -2
---
inverse of system matrix
0.6 -0.8 0.8
-0.4 1.2 -0.2
-0.2 0.6 -0.6
---
determinant of system matrix = -5
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php