### CHECK OUT SHMOOP'S FREE STUDY TOOLS:

# Systems of Linear Equations

### CHECK OUT SHMOOP'S FREE STUDY TOOLS:

# Systems of Linear Equations Examples

#### Solving Systems of Linear Equations by Graphing

The solution(s) to a system of linear equations are all the point(s) where the lines intersect. To solve a system by graphing, we graph the lines and see where they meet up. Are they grabbing a cou...

#### Solving Systems of Linear Equations by Substitution

To solve linear systems by substitution, we solve one equation for one variable and then use that information to solve the other equation for the other variable. It's exactly the same as w...

#### Solving Systems of Linear Equations by Addition

When we have two equations, we can add them together to get a new equation. We don't even need to ask for their consent. Ifa = band c = d,we can add the left-hand sides of the equations and the rig...

#### More Vocabulary

We know how to solve a system of two linear equations, not to mention what a system of equations actually looks like. We also know that a system of two linear equations has 0, 1, or infinitely many...

#### Word Problems and Lines

Lots of word problems can be solved with systems of linear equations. However, before we bother with those, let's look at some word problems that describe single lines, and we're not referring to o...

#### Translating a Word Problem into a System of Equations

To describe a word problem using a system of equations, we need to figure out what the two unknown quantities are and give them names, usually x and y. We could name them Moonshadow and Talulabelle...