# Systems of Linear Equations Exercises

#### Systems of Equations

A system of equations is a group of two or more equations. What, you were expecting robots?Sample ProblemJust to get your feet wet, here's a system of two equations:Another Sample ProblemThe thr...

#### 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 when a...

#### 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 permission. Let's say we're trying to solve the following system:a = bc = dWe can a...

#### Solving Linear Systems

Now, of course, comes the big question: if we're asked to solve a system of linear equations and not told how, which method do we use? Oh, sorry. No, we're not going to ask you to prom. We meant...

#### Solving Word Problems

Now that we've practiced turning words into linear equations, let's actually solve a couple of word problems. This is usually a three-step process:Find the linear equation being described. Figure...

#### Word Problems with Two Lines

Now we'll move on to some word problems that involve finding where two lines intersect—in other words, solving a system of equations. We'll start with word problems that are obvious about descr...

#### 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 Talulabel...

#### Solving Word Problems with Systems of Equations

The best way to learn how to solve a word problem is to do it. Same goes for freestyle swimming, riding a bike, or writing a book about the ideological origins of the American Revolution. Okay, a...