## Solving Systems of Linear Equations

#### Common Questions

#### 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 $(y=mx+b)$.

For example, $4x+2y=8$ is a linear equation. If we rearrange the equation and isolate $y$, we can see that $4x+2y=8$ is equivalent to $y=−2x+4$.

Read below to learn more.

#### 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 $75%$ 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 $x$ and $y$ 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!

Method | Pros | Cons |
---|---|---|

Substitution Method | Easier when one of the variables has a coefficient of $1$. Example: - $3x+y=4$
- $2x+2y=4$
| Might need to use fractions if no variables have a coefficient of $1$ |

Elimination Method | Easier if both equations have the same term Example: - $4x+3y=11$
- $2x+3y=7$
| 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 Example: - $y=2x+1$
- $y=−x+2$
| Difficult to use when the solution is large or is a fraction |