Page 2: Solving Systems of Equations

This page covers two main methods for solving system of equations: substitution and elimination, providing detailed explanations of each approach.

Definition: Substitution method involves solving one equation for a variable and inserting that expression into the other equation to solve the system.

Highlight: When solving a system with two variables, the solution should be written as an ordered pair, following standard mathematical convention.

Example: The elimination method involves combining equations to create new equations with fewer variables, making the system easier to solve.

Vocabulary: Key terms for solving systems:

• Substitution: replacing variables with equivalent expressions
• Elimination: combining equations to remove variables

Quote: "When using elimination, look for the easiest variables to eliminate first."

Highlight: The elimination method is particularly effective for solving nonlinear equations, but should be used strategically rather than arbitrarily eliminating variables.

Page 1: Understanding Inequalities and Their Properties

This page introduces fundamental concepts of solving inequalities algebra 1 and explains key notation systems. The isolation method is presented as the primary approach for solving both equations and inequalities.

Definition: Strict inequalities indicate that two sides cannot be equal, while non-strict inequalities allow the sides to be equal.

Example: When solving an equation like 5r-2=10-r, you can verify the solution by substituting it back into the original equation:

• 6r-2=10
• r=2

Highlight: When multiplying or dividing an inequality by a negative number, you must reverse the direction of the inequality sign - this is a crucial solving inequalities rule.

Vocabulary: Interval notation components:

• () indicates values not included
• [] indicates values are included
• E represents "is in"
• -∞ represents negative infinity
• +∞ represents positive infinity
• R represents all real numbers

Example: Interval notation examples:

• TE[3,5) means 3≤t<5
• TE(4,∞) means t>4