MYP Standard Mathematics Linear Equations Notes

1. Linear equations are one of the most important mathematical models you use to describe relationships where change is constant.
2. In this topic, you will focus on solving linear equations in a way that is logically justified, using equivalence transformations (steps that keep the solution set the same), and you will connect algebraic solutions to graphical ones.

Linear Equations Describe A Balance

A linear equation is an equation in which the variable(s) appear only to the power 1, and are not multiplied together.

What makes an equation an equation (not just an expression) is the equals sign, which represents a balance: both sides have the same value.

The key idea in solving linear equations is to perform operations that produce equivalent equations, so you never "change the answer set" while you simplify.

Equivalence Transformations Preserve Solutions

1. An equivalence transformation is a change you make to an equation that results in an equivalent equation (same solution set).
2. The most common equivalence transformations are based on two principles.

These principles justify the standard steps you already use, such as "add 5 to both sides" or "divide both sides by 3".

Distributive And Simplifying Steps Still Matter

1. Not every step you do is an "addition" or "multiplication" principle step.
2. Sometimes you are using algebraic properties to rewrite expressions without changing their value.
3. For example, expanding brackets uses the distributive property: $$2(3x-4)=6x-8$$
4. That rewriting does not change the equation, it just expresses the same left-hand side more simply.