# Solve System of Equations in R

In this article, we will discuss how to solve a system of equations in R Programming Language.

**solve()** function in R Language is used to solve the equation. Here equation is like a*x = b, where b is a vector or matrix and x is a variable whose value is going to be calculated.

Syntax:solve(a, b)

Parameters:

a:coefficients of the equationb:vector or matrix of the equation

**Example 1: Solving system equation of three equations**

Given Equations:x + 2y + 3z = 20 2x + 2y + 3z = 100 3x + 2y + 8z = 200Matrix A and B for solution using coefficient of equations:A-> 1 2 3 2 2 3 3 2 8 B-> 20 100 200

To solve this using two matrices in R we use the following code:

## R

`# create matrix A and B using given equations` `A <- ` `rbind` `(` `c` `(1, 2, 3), ` ` ` `c` `(2, 2, 3), ` ` ` `c` `(3, 2, 8))` `B <- ` `c` `(20, 100, 200)` ` ` `# Solve them using solve function in R` `solve` `(A, B)` |

**Output:**

80 -36 3.99999999999999

which means x=80, y=-36 and z=4 is the solution for linear equations.

**Example 2: Solving system equation of three equations**

To get solutions in form of fractions, we use library MASS in R Language and wrap solve function in fractions.

Given Equations:19x + 32y + 31z = 1110 22x + 28y + 13z = 1406 31x + 12y + 81z = 3040Matrix A and B for solution using coefficient of equations:A-> 19 32 31 22 28 13 31 12 81 B-> 1110 1406 3040

To solve this using two matrices in R we use the following code:

## R

`# Load package MASS` `library` `(MASS)` ` ` `# create matrix A and B using given equations` `A <- ` `rbind` `(` `c` `(19, 32, 31), ` ` ` `c` `(22, 28, 31), ` ` ` `c` `(31, 12, 81))` `B <- ` `c` `(1110, 1406, 3040)` ` ` `# Solve them using solve` `# function wrapped in fractions` `fractions` `(` `solve` `(A, B))` |

**Output:**

[1] 159950/2243 -92039/4486 29784/2243

which means x=159950/2243 , y=-92039/4486 and z=29784/2243 is the solution for the above given linear equation.

**Example 3: Solving Inverse matrix**

## R

`# create matrix A and B using given equations` `A <- ` `matrix` `(` `c` `(4, 7, 3, 6), ncol = 2)` `print` `(A)` ` ` `print` `(` `"Inverse matrix"` `)` ` ` `# Solve them using solve function in R` `print` `(` `solve` `(A))` |

**Output:**

[,1] [,2] [1,] 4 3 [2,] 7 6 [1] "Inverse matrix" [,1] [,2] [1,] 2.000000 -1.000000 [2,] -2.333333 1.333333