# Systems of Linear and Quadratic Equations Worksheets

With this section we explore when a linear and quadratic equation form a system. If you remember back, a system is where those two equations share the same set of variables. In this section we will go over several different techniques that you can use to solve those system. When we solve them, we are determining the value of those variables. You can use algebra or graphing. In many cases one method is more practical then the other. We will explore many worksheet based problems that will help you learn which of those two methods is better for each situation.

### Aligned Standard: HSA-REI.C.7

- Equal to "y" Step-by-step Lesson- My high school teacher always taught use to double it down. Little did I know that was a gambling reference.
- Guided Lesson - I put the bottom two in bold to help you conserve paper. You can work right off of them in the way that they are ordered.
- Guided Lesson Explanation -Make everything equal to y and go from there.
- Practice Worksheet - There should be plenty of work space on this sheet for you and students alike.
- Matching Worksheet - Find the matching values for each system setup.

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

### Homework Sheets

Superman would be proud of you with this homework.

- Homework 1 - Let's start by getting both equations to equal y. The first equation is set to equal y.
- Homework 2 - Start by rearranging what you are presented with.
- Homework 3 - Solve the following simultaneous equations by graphing.

### Practice Worksheets

I tried to show a number of different methods for answering these.

- Practice 1 - Set them equal to each other, that will show them.
- Practice 2 - I would go after the non-squared value, but it is your choice.
- Practice 3 - Where do they meet on a graph?

### Math Skill Quizzes

Sometimes we solve a system and other times you solve a single equation.

- Quiz 1 - A real well thought out run through for you.
- Quiz 2 - Factor the expressions.
- Quiz 3 - Think of how best to approach this one.

### What are Systems of Simultaneous Equations?

Ever noticed a statement or an expression with alphabets and numbers written together? Something like: 6a + 5b = 4. In mathematics, we term such expression as equations. A statement in which two mathematical expressions like (6a) and (5b) represent an unknown variable that contains a multiplier. But these equations are not always singular. They can be in a set of two or more equations. When equations are presented in a set of two or more than two equations, we call them as simultaneous equations. Each equation shares their variables whose values need to satisfy the equations in the set simultaneously.

Simultaneous equations often come in two different forms: **linear** or **quadratics**.

A linear equation is also known as a first-degree equation, which means that the highest power of the variable in any linear equation is one. Even in the case of two variables, each variable of a linear equation has the power of one. When you graph lines of these types of equations, they form a perfectly straight line.

Unlike linear equations, quadratic equations have at least one variable squared, i.e., raised to the second power. For example: 6x^{2} + 7y = 5 or 3a^{2} + 4b^{2} + 2 = 1. When you graph quadratics, they form a parabola on a graph. That is the (U) shape in some orientation.

There are many situations where a linear and quadratic equation can form a system. We will often be asked to solve these types of systems. That means to determine the values of the variables that they share. There are several ways you can go about both graphically and with the help of algebra. I also find plot these equations on graphs is always my first choice. You just need to spot the location or locations where they intersect. Those intersection points are values of the variables. Graphing is not always practical for all situations; in those cases, we can use algebra. The common algebraic progression has you rewrite both equations in the (y =) format and set them equal to one another. You can solve the quadratic by using the standard quadratic formula. This will give you the x and y values.