# Homework 1 Solving Systems By Graphing Worksheet

A system of linear equation comprises two or more linear equations. The solution of a linear system is the ordered pair that is a solution to all equations in the system.

One way of solving a linear system is by graphing. The solution to the system will then be in the point in which the two equations intersect.

**Example**

Solve the following system of linear equations

$$\left\{\begin{matrix} y=2x+4\\ y=3x+2 \end{matrix}\right.$$

The two lines appear to intersect in (2, 8)

It's a good idea to always check your graphical solution algebraically by substituting x and y in your equations with the ordered pair

$$\underline{y=2x+4} \\ {\color{green} 8}\overset{?}{=} 2\cdot {\color{green} 2}+4$$

$$8=8$$

$$\underline{y=3x+2}$$

$${\color{green} 8}\overset{?}{=}3\cdot {\color{green} 2}+2$$

$$8=8$$

A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct.

Linear systems composes of parallel lines that have the same slope but different y-intersect do not have a solution since the lines won't intersect. Linear systems without a solution are called inconsistent systems.

Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems. Consistent dependent systems have infinitely many solutions since the lines coincide.

**Video lesson**

Solve the linear system graphically

$$\left\{\begin{matrix} 2y - 4x = 2 \\ y = -x + 4\\ \end{matrix}\right.$$

Share on Facebook

Product Description

This bundle contains notes, homework, three quizzes, a study guide, and a test that cover the following topics:

• Solving Systems of Equations by Graphing

• Solving Systems of Equations by Substitution

• Solving Systems of Equations by Elimination

• Comparing Methods to Solving Systems/Review of All Methods

• Systems of Equations Word Problems

• Solving Systems of Equations by Matrices

• Linear Inequalities

• Systems of Linear Inequalities

• Systems of Linear Inequalities Word Problems

Please download the preview to see a sample outline along with a collage of some of the pages.**NEW: Assessments are now EDITABLE!** Now you can easily make multiple versions or customize to fit your needs! PowerPoint and Equation Editor (usually built in to PowerPoint) are required to edit these files. There is a folder titled "Editable Assessments" when you download. This is where you will find editable versions of each quiz and the unit test. If your Equation Editor is incompatible with mine, simply delete my equation and insert your own.**This resource is included in the following bundle(s):Algebra 1 First Semester Notes BundleAlgebra 1 Curriculum**

**More Algebra 1 Units:**

Unit 1 – Algebra Basics

Unit 2 – Multi-Step Equations & Inequalities

Unit 3 – Relations & Functions

Unit 4 – Linear Equations

Direct & Inverse Variation (Mini-Unit)

Unit 6 – Exponent Rules

Unit 7 – Polynomials & Factoring

Unit 8 – Quadratic Equations

Unit 9 – Statistics

Unit 10 – Rational Expressions & Equations

Unit 11 – Radical Expressions & Equations

Unit 1 – Algebra Basics

Unit 2 – Multi-Step Equations & Inequalities

Unit 3 – Relations & Functions

Unit 4 – Linear Equations

Direct & Inverse Variation (Mini-Unit)

Unit 6 – Exponent Rules

Unit 7 – Polynomials & Factoring

Unit 8 – Quadratic Equations

Unit 9 – Statistics

Unit 10 – Rational Expressions & Equations

Unit 11 – Radical Expressions & Equations

**LICENSING TERMS:**This purchase includes a license for

**one teacher only**for personal use in their classroom. Licenses are

**non-transferable**, meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at allthingsalgebra@gmail.com.

**COPYRIGHT TERMS:**This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

Teaching Duration

1 month

## 0 comments