Equations and Inequalities Quiz

Questions and Answers

ax + by = c

Synthesis

All real numbers

y = mx + b Signup and view all the answers

2x + 3 > 5 Signup and view all the answers

(3/2, 0) Signup and view all the answers

f(g(x)) = 4x^2 Signup and view all the answers

Vertical line Signup and view all the answers

Study Notes

An equation is a statement that says two expressions are equal.
Equations can be linear (degree 1) or nonlinear (degree 2 or higher).
Linear equations can be written in the form: ax + by = c, where a, b, and c are constants.
Equations can be solved using various methods, including:
- Addition and subtraction
- Multiplication and division
- Substitution
- Elimination

An inequality is a statement that says two expressions are not equal.
Inequalities can be linear or nonlinear.
Linear inequalities can be written in the form: ax + by > c, ax + by < c, ax + by ≥ c, or ax + by ≤ c.
Inequalities can be solved using various methods, including:
- Graphing on a number line
- Testing points
- Solving related equations

A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
Functions can be represented algebraically, graphically, or numerically.
Function notation: f(x) = ... or y = ...
Key concepts:
- Domain and range
- Function operations (addition, subtraction, multiplication, division)
- Composition of functions

A system of equations is a set of two or more equations with two or more variables.
Systems can be solved using various methods, including:
- Substitution
- Elimination
- Graphing
Types of systems:
- Independent systems (unique solution)
- Dependent systems (infinite solutions)
- Inconsistent systems (no solution)

Graphing is a visual representation of equations and functions on a coordinate plane.
Key concepts:
- x-axis (horizontal) and y-axis (vertical)
- Quadrants (I, II, III, IV)
- Intercepts (x-intercept, y-intercept)
- Slope and steepness
Graphing methods:
- Plotting points
- Using slope-intercept form (y = mx + b)
- Using standard form (Ax + By = C)

Equations are statements that express the equality of two expressions.
They can be classified as linear (degree 1) or nonlinear (degree 2 or higher).
Linear equations can be written in the form ax + by = c, where a, b, and c are constants.
Various methods can be used to solve equations, including:
- Addition and subtraction
- Multiplication and division
- Substitution
- Elimination

Inequalities are statements that express the non-equality of two expressions.
Like equations, they can be linear or nonlinear.
Linear inequalities can be written in the form ax + by > c, ax + by < c, ax + by ≥ c, or ax + by ≤ c.
Inequalities can be solved using various methods, including:
- Graphing on a number line
- Testing points
- Solving related equations

Functions are relations between a set of inputs (domain) and a set of possible outputs (range).
They can be represented algebraically, graphically, or numerically.
Function notation: f(x) =... or y =....
Key concepts:
- Domain and range
- Function operations (addition, subtraction, multiplication, division)
- Composition of functions

Systems of equations consist of two or more equations with two or more variables.
Systems can be solved using various methods, including:
- Substitution
- Elimination
- Graphing
Types of systems:
- Independent systems (unique solution)
- Dependent systems (infinite solutions)
- Inconsistent systems (no solution)

Graphing is a visual representation of equations and functions on a coordinate plane.
Key concepts:
- x-axis (horizontal) and y-axis (vertical)
- Quadrants (I, II, III, IV)
- Intercepts (x-intercept, y-intercept)
- Slope and steepness
Graphing methods:
- Plotting points
- Using slope-intercept form (y = mx + b)
- Using standard form (Ax + By = C)