Solving a system of equations algebraically is like solving a riddle. Each linear equation provides a clue needed to solve for the mystery values of each variable.

Just like the answer to a mystery must agree with each clue, the values of each variable in a system of equations must agree with each equation in the system.

This means that once we find the values that make every equation in the system true at the same time, we have our solution.

Consider the following system of equations:

$x+yx+3y =6=16 $We can solve the systems of equations by :

We typically see systems of linear equations with one solution, but they can also have no solutions or infinite solutions depending on *if* and *how* the lines of the equations intersect.

### How do we solve a system of linear equations by graphing?

To solve a system of linear equations using the graphing method, we simply need to graph each equation in the system and find the point where all the lines intersect.

For example, we can see that the solution to the following system of equations is $(0,5)$:

$x+yx+3y =5=15 $Check out our lesson to learn more!You can also use the Quick Links menu on the left to jump to a section of your choice.

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## Systems of Linear Equations Calculator

## How to Solve a System of Linear Equations Algebraically

Solving a System of Linear Equations by