Podcast
Questions and Answers
What is the condition for a linear equation in one variable to have a unique solution?
What is the condition for a linear equation in one variable to have a unique solution?
- a = 0
- a ≠ 0 (correct)
- b ≠ c
- a > 0
What is the first step in solving a linear equation?
What is the first step in solving a linear equation?
- Add or subtract the same value to both sides of the equation to isolate the term with the variable (correct)
- Multiply both sides of the equation by the coefficient of the variable
- Subtract the variable from both sides of the equation
- Divide both sides of the equation by the coefficient of the variable
What is the graphical representation of a linear equation in one variable?
What is the graphical representation of a linear equation in one variable?
- A parabola on the coordinate plane
- A straight line on the number line (correct)
- An ellipse on the coordinate plane
- A circle on the coordinate plane
What is the slope of the line representing a linear equation in one variable?
What is the slope of the line representing a linear equation in one variable?
What happens to a linear equation in one variable if a = 0 and b = c?
What happens to a linear equation in one variable if a = 0 and b = c?
What is the purpose of dividing both sides of the equation by the coefficient of the variable?
What is the purpose of dividing both sides of the equation by the coefficient of the variable?
Study Notes
Definition and Notation
- A linear equation in one variable is an equation that can be written in the form
ax + b = c, where:a,b, andcare constantsais the coefficient of the variablexxis the variable
Properties
- A linear equation in one variable has a unique solution if
a ≠ 0 - If
a = 0, the equation is a linear equation in one variable only ifb = c, in which case it has infinitely many solutions - If
a = 0andb ≠ c, the equation has no solution
Solving Linear Equations
- To solve a linear equation, isolate the variable
xby performing the following steps:- Add or subtract the same value to both sides of the equation to isolate the term with the variable
- Divide both sides of the equation by the coefficient of the variable (
a) to solve forx
- Example:
2x + 3 = 7- Subtract 3 from both sides:
2x = 4 - Divide both sides by 2:
x = 2
- Subtract 3 from both sides:
Graphical Representation
- The graph of a linear equation in one variable is a straight line on the number line
- The line intersects the
x-axis at the solution to the equation - The slope of the line is the coefficient of the variable (
a)
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Description
Learn about the definition, properties, and solving methods of linear equations in one variable. Understand how to isolate the variable and graph the equation on the number line.
