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# Solving System of Equations

A system of equations refers to a set of two or more equations that has common solutions. This means for certain values of the variables, both the equations will be true. The purpose of solving system of equations is to find the values of the variables that satisfy the conditions of all the given equations. A system of equations can be solved by various methods. To solve a system of equations involving two variables, we need to solve two equations. The most common methods to solve systems of equations with two variables are as follows:

• Substitution method.
• Elimination method.
• Graphical method

## Substitution Method

Using any one of the equations, one variable is expressed in the form of other variables and constants. Then that value is substituted for another variable in the second equation. The second equation thus consists of only one variable and can be solved to find the value of that variable. This numerical value is substituted in any of the original equations and solved to get the value of the other variable.

### Elimination Method

In this method, both equations are multiplied by different suitable numbers so that the coefficients of one of the variables become the same in both equations. Then by subtracting the equations, one of the variables is eliminated and a third equation is obtained with only one variable. This equation is solved for that variable and the value thus obtained is put into any of the original equations to find the value of the other variable.

### Graphical Method

In the graphical method, graphs are plotted for both by assigning different values to the variables. The two graphs as drawn are found to be intersected at a point. The coordinate of the point of intersection represents the values of the variables.

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