**Algebra
Systems of Equations**

The primary goal for the first semester of Algebra in the 8th or 9th grade is to prepare students to solve a system of equations. During the first semester of secondary algebra, the foundations provide the skill for students to understand linear equations. In order to master the systems of equations a student must understand and master underlying skills such as the order of operations and the distributive property. These necessary skills are to help students to transform equations (rewrite them. This should be a fun activity because it is a hands on activity facilitated through graphing points on a coordinate plane. Students learn about the quadrants (places on a graph) and those they only need two points to graph a line. This is an important postulate in a later course of geometry. There can exist only one line through any two points within a coordinate plane (Euclidean Geometry).

**Algebra Systems
of Equations –Key Concepts**

The concepts that need to be mastered are as follows: ·

- Understand the slope, derive from a graph or algebraically through two ordered pairs (two points on a graph), use a table of values (input/output tables for a constant rate of change), and the rise over run.
- Understand how to graph a linear equation from the slope-intercept, standard, and point-slope forms of linear equations. ·
- Understand how to transform linear equations from the slope intercept from into the standard form and the point-slope form. ·
- Understand the different looks of a positive, negative, zero, and undefined slope of a linear equation. ·
- Understand how to find on a graph the x and y intercepts of a line.
- Understand how to find the x and y intercepts from an equation of a line.
- (Slope intercept, standard form, and the point-slope form).
- Memorize and know the different forms of linear equations.
- Understand the relationships of the slopes of parallel and perpendicular lines.
- Understand how to determine if there is one, none, or infinite solutions in a system of linear equations.
- Understand what a solution to a system of linear equations looks like algebraically and graphically.

**Other Systems of Equations – Online Resources**

**Other Algebra Resources**

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