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# Solving Systems of Linear Equations

#### What is a system of linear equations?

Great question! A system of linear equations is a set of two or more linear equations. Keep in mind that linear equations don’t always present themselves in slope-intercept format .

For example, is a linear equation. If we rearrange the equation and isolate , we can see that is equivalent to .

#### Common Questions   ### What is a System of Linear Equations?

A system of linear equations is a set of two or more linear equations.

Solving a system of equations is like making plans with a friend. Each linear equation is like a rule, and we use a "system" when we have multiple rules that we need our variables to follow.

For example, if you're picking a movie to watch with a friend, you might have multiple rules like "no horror movies," "must have some action," and "must have at least a on Rotten Tomatoes."

Our variables are like the movie and our equations are like the rules. When you want to watch a movie with friends, you want to find one that satisfies all the rules. Similarly, when we solve a system of equations, we want to find values for and that satisfy both equations. There are a few different ways we can solve a system of linear equations. A system of equations can be solved using any of these methods, but there are certain situations where one method is easier to use!

MethodProsCons
Substitution MethodEasier when one of the variables has a coefficient of .

Example:
Might need to use fractions if no variables have a coefficient of
Elimination MethodEasier if both equations have the same term

Example:
Might need to multiply one or both equations by constants to get terms with matching coefficients
Graphing MethodEasier if both equations are in slope-intercept form

Example:
Also useful for finding number of solutions
Difficult to use when the solution is large or is a fraction