## Solving Simultaneous Equations (Linear and Quadratics)

#### Aligned To Common Core Standard:

**High School** - HSA-REI.C.7

What are Simultaneous Equations (Linear and Quadratics)?
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' are referred as equal.
But these equations are not always singular. They can be in a set of two or more equations.
**SIMULTANEOUS 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.
Types of Simultaneous Equation
Simultaneous equations are classified as
**Linear Equation** or **Quadratic Equation**
Let's briefly discuss each type. **LINEAR EQUATION** - 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. For example;
x + 9 = 5
in case of more than one variable, linear equations are written as:
5x + 2y + 6 = 1
Notice that the power of every variable is 1
**QUADRATIC EQUATION** - 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

### Printable Worksheets And Lessons

- 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.

- Linear Quadratic Systems-
Emphasis on Graphing Five Worksheet Pack - We give you two systems
and ask you five questions each on them.

#### 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.