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

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

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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 Bundle
Algebra 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


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Teaching Duration

1 month

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