Unit 3

Initial value

In mathematics, in the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.

Substitution

Substitution "Substitute" means to put in the place of another

Slope intercept form

The Meaning of Slope and y-Intercept. in the Context of Word Problems. In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept, where the line crosses the y-axis.

Non-linear

not denoting, involving, or arranged in a straight line.

One solution

Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. With a system of equations or system of inequalities, the solution set is the set containing value(s) of the variable(s) that satisfy all equations and/or inequalities in the system.

Combine like terms

Are all like terms because the variables are all xy 2 Unlike terms If they are not like terms, they are called " Unlike terms

System of equations

Common Variables For the equations to "work together" they share one or more variables:

Constant rate of change

Definition 2 (Constant rates of change) The (constant) rate of change with respect to the variable x of a linear function y = f(x) is the slope of its graph.

Coefficient

Definition of Coefficient more ... A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a Coefficient. Sometimes a letter stands in for the number.

Constant

Definition of Constant more ... A fixed value. In Algebra, a Constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Term

Definition of Term more ... In Algebra a Term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs See: Variable Algebra

Variable

Definition of Variable more ... A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the Variable.

Distributive property

In general, this term refers to the distributive property of multiplication which states that the. Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Unit rate

In math, the unit rate is a comparison of two different quantities when they are combined together. Discover the definition of the unit rate in math with tips from a mathematics tutor in this free video on math lessons

Elimination

Eliminate" means to remove

Expression

Expression more ... Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

Slope

How steep a straight line is. In this example the slope is 3/5 = 0.6

Infinitely many solutions

Infinite solutions would mean that any value for the variable would make the equation true.

Infinite solution

Infinite solutions would mean that any value for the variable would make the equation true. No Solution Equations. Let's look at the following equation: Note that we have variables on both sides of the equation. So we'll subtract from both sides to eliminate the on the right side of the equation.

No solution

No solution would mean that there is no answer to the equation.

Proportions

Proportion says that two ratios (or fractions) are equal.

Inverse operation

The operation that reverses the effect of another operation.

Equation

a statement that the values of two mathematical expressions are equal

Y-intercept

Y Intercept more ... Where a straight line crosses the Y axis of a graph.

Linear

arranged in or extending along a straight or nearly straight line.