# Solving system of linear equations

### Solution:

2/3a+1c =12/3b + 1d =0

-3a + 1/3c =0

-3b + 1/3d =1

2/3·a+1·c =1

2/3·b + 1·d =0

-3·a + 1/3·c =0

-3·b + 1/3·d =1

2a+3c = 3

2b+3d = 0

9a-c = 0

9b-d = -3

Pivot: Row 1 ↔ Row 3

9a-c = 0

2b+3d = 0

2a+3c = 3

9b-d = -3

Row 3 - 2/9 · Row 1 → Row 3

9a-c = 0

2b+3d = 0

3.2222c = 3

9b-d = -3

Pivot: Row 2 ↔ Row 4

9a-c = 0

9b-d = -3

3.2222c = 3

2b+3d = 0

Row 4 - 2/9 · Row 2 → Row 4

9a-c = 0

9b-d = -3

3.2222c = 3

3.2222d = 0.6667

d = 0.66666667/3.22222222 = 0.20689655

c = 3/3.22222222 = 0.93103448

b = -3+d/9 = -3+0.20689655/9 = -0.31034483

a = 0+c/9 = 0+0.93103448/9 = 0.10344828

a = 3/29 ≈ 0.103448

b = -9/29 ≈ -0.310345

c = 27/29 ≈ 0.931034

d = 6/29 ≈ 0.206897

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

### Our mission:

Provide simple, fast, and reliable mathematical service for solving any equation(s).### More info:

Unknowns (variables) write as one character a-z, i.e., a, b, x, y, z. No matter whether you want to solve an equation with a single unknown, a system of two equations of two unknowns, the system of three equations and three unknowns, or a linear system with twenty unknowns. The number of equations and the number of unknowns should be equal, and the equation should be linear (and linear independent). Then you can be expected that the equations have one solution.It is not necessary to write equations in the basic form. The calculator quickly performs equivalent operations on the given linear system.