# Solving Systems of Equations Worksheets

There are systems of linear equation where two or more of these equations work together. This means that they have the values for the unknown variables within them. So, if one equation has a variable named x that we find to have a value of 5, all the other equations in the system that have the variable x present also have a value of 5 for the x variable. There are a number of different methods that can be used to determine these values in systems of equations. This collection of worksheets and lessons will show you various methods to help you find these unknown variables within systems of equations.

### Aligned Standard: HSA-REI.C.5

- Using Elimination Step-by-step Lesson- You will need plenty of scrap paper for this unit.
- Guided Lesson - We go over both the use of elimination and substitution to solve these systems.
- Guided Lesson Explanation - Each explanation requires it's own page; like we said, "Bring on the scrap paper supply!".
- Practice Worksheet - We do give you a direction to go in to solve each of the problems.
- Matching Worksheet - Match each system to its solution.
- Linear Systems - Write as a Linear Equation Five Pack - You start with a matrix and have to derive a linear equation from it.
- Algebraic Solutions to Simultaneous Equations Five Pack - It is always fun when you need to find both x and y.
- Algebraic Solutions to Linear Systems Five Pack - Very similar to the previous 5 pack, but a whole new line of questioning.
- Linear-Quadratic Systems Five Pack - We ask you to focus on algebra strategies to solve this one.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

There are many different ways to solve systems. This standard should be renamed.

- Homework 1 - Solve the system using elimination.
- Homework 2 - Solve the system using substitution.
- Homework 3 - The variable y is already isolated in the second equation. Plug the result of Step 1 into the other equation and solve for one variable.

### Practice Worksheets

I'm not sure that you can mark a paper wrong, if they solve it graphically .

- Practice 1 - Plug the result of Step 1 into one of the original equations and solve for the other variable.
- Practice 2 - Make sure the equations have opposite x terms or opposite y terms.
- Practice 3 - Add to eliminate one variable and solve for the other. Add to eliminate the y terms, and then solve for x.

### Math Skill Quizzes

I find this skill to really show you the plane that kids think on when solving problems.

- Quiz 1 - Use the elimination method here to finish off all of these exercises.
- Quiz 2 - Write the system of linear equations represented by each matrix equation. You will also solve polynomials.
- Quiz 3 - No need to worry about graphs here. You will cover all the major skills that we have learned on this topic.
- Quiz 4 - You will use several methods to approach and find the missing values of x and y.
- Quiz 5 - Another quiz requiring the use of multiple techniques to solve. Created by member request.

### How to Solve Systems of Equations

The basic concept of mathematics when you try to learn about the equations is the system of equations. As the name implies, a system of equations is indeed a system that involves 2 or more equations in it. The system of equations involves solving 2 linear equations simultaneously. This means that your equations will most probably have two variables; one, x-variable, and second, y-variable. Because the equations are a system these unknown variables have the same value. When we are attempting to solve these systems, we are looking the value of those unknown variables.

There are several methods to solve systems of equations, which you might have to use in the near future you'll encounter more complicated problems involving the system of equations. Which method you decide to use really is depending on how they equations present themselves and there is no one best method to always use. Now let's get straight to how we can solve systems of equations.

**1. The Graphing Method** - Visuals can make comprehending things easy. A visual and easiest way to solve a system of equations is to plot them on a graph. When we they are graphed we are looking for the point(s) that they intersect at. Those points indicate the solution.

**2. The Substitution Method** - Since graphing is not a very effective way to solve these equations consistently, the substitution method is another method that is more commonly used. It is the best method to isolate one variable. This method helps you to work with only one variable. Once you know the value of one variable, plug the value of the variable in the other equation to find out the other variable. One variable, you can easily find the value of the other variable by back-solving.

**3. The Elimination Method** - It is strategically eliminating a variable by performing addition over these two equations together. Multiply one or both equations by value to eliminate a variable. This way, you'll end up with a one-variable equation, and then you will find the value of the other variable easily.