# solve system of linear equations

## Calculus solve_system

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### Function : solve_system

#### Summary :

The solve_system function allows to solve equations with several unknowns: Equation 2 unknown systems, systems of equations with 3 unknown in n unknowns systems.

solve_system online

# Solving systems of equations online

Solving equations with several unknowns in other words, solving system of equations online is possible through the use of the function solve_system of the calculator. The calculator allows the resolution system online of several types, it is possible :

• to solve systems of equations with two unknown online,
• to solve systems of equations with three unknowns online,
• and more generally, the resolution of online systems equation with several unknowns.

With its ability to algebra, the calculator can solve equations with two unknown or solve equations with 3 unknowns involving letters (literal calculation).

The calculator is an equation system solver that uses a very simple syntax to solve systems of linear equations that admit a single solution.

## Solving a system of 2 equations with 2 unknowns

There are several methods to solve a system of 2 equations with 2 unknowns: the substitution method, the combination method, the graphical method, Cramer's method.

• The combination method consists in eliminating one of the variables thanks to arithmetic operations on the equations;
• The substitution method consists of expressing one of the variables as a function of the other and then replacing to arrive at an equation with one unknown;
• The method of graphically solving makes it possible to conjecture the solution which will have to be verified by the calculation, the graphical method consists in representing the straight lines which correspond to the equations, then "reading" the coordinates of the point of intersection, the graphical calculator makes it possible to carry out this type of operation;
• Cramer's method uses determinants.

The calculator can use these methods to solve equations with 2 unknowns

To solve the system of 2 equations with 2 unknowns according to x+y=18 and 3*y+2*x=46, it is necessary to enter solve_system([x+y=18;3*y+2*x=46];[x;y]) ,after calculation, the result [x=8;y=10] is returned.

## Solving a system of 3 equations with 3 unknowns

To find the solutions of the systems of 3 equations with 3 unknowns the calculator can use the substitution method, the combination method or the Cramer method.

Thus for example, to solve the linear system of equations according to x+y+z=1, x-y+z=3, x-y-z=1, it is necessary to enter solve_system([x+y+z=1;x-y+z=3;x-y-z=1];[x;y;z]) , after calculation, the result [x=1;y=-1;z=1] is returned.

The solve_system function allows to solve equations with several unknowns: Equation 2 unknown systems, systems of equations with 3 unknown in n unknowns systems.

#### Syntax :

solve_system([equation1;equation2;...;equationN];[variable1;variable2...variableN])

#### Examples :

• x+y=18
• 3*y+2*x=46
solve_system([x+y=18;3*y+2*x=46];[x;y]), returns[x=8;y=10]

Calculate online with solve_system (solve system of linear equations)