In this article, we will discuss solving 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 equation**b:**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:

```
# 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

**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

Related post: Solving a System of Equations in Pure<br>Python without Numpy or Scipy