# Solving system of linear equations

### Solution:

170 =x+y+z
x =14+y
y =z- z/5

x+y+z = 170
x-y = 14
5y-4z = 0

Row 2 - Row 1 → Row 2
x+y+z = 170
-2y-z = -156
5y-4z = 0

Pivot: Row 2 ↔ Row 3
x+y+z = 170
5y-4z = 0
-2y-z = -156

Row 3 - -2/5 · Row 2 → Row 3
x+y+z = 170
5y-4z = 0
-2.6z = -156

z = -156/-2.6 = 60
y = 0+4z/5 = 0+4 · 60/5 = 48
x = 170-y-z = 170-48-60 = 62

x = 62
y = 48
z = 60

Write each equation on a new line or separate it by a semicolon. The online calculator solves a system of linear equations (with 1,2,...,n unknowns), quadratic equation with one unknown variable, cubic equation with one unknown variable, and finally, any other equation with one variable. Even if an exact solution does not exist, it calculates a numerical approximation of roots.

### Examples:

```a+b = 12
a-3b = a-b+43```
```x+y+z=100
3x-6y+2z=50
y-3z+x=(44-22)x+45```
`(x+4)(x-3)+34x+6x^2 = 256`
`(x+4)+34x+x^2-x^3 = -32`
`ln x = 1.2-x`
`sin x = cos(x-pi/3)+x`
`sin x = x^3+2x+x-1`
`sin x = 0.5`
`(cos x)^2 = tan(x-pi/3)`
`x^5+x^4 = -23+sin x`
`|log x|=2`
`|ln x+1|=x/10`
`|ln x+1|=ln x^2`
`1/(x+2)=1/x+4`
`sqrt(x^4+x^2+2)=22`

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