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 .
Read below to learn more.
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!
|Substitution Method||Easier when one of the variables has a coefficient of .|
|Might need to use fractions if no variables have a coefficient of|
|Elimination Method||Easier if both equations have the same term|
|Might need to multiply one or both equations by constants to get terms with matching coefficients|
|Graphing Method||Easier if both equations are in slope-intercept form|
|Difficult to use when the solution is large or is a fraction|