Systems Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method where one equation is manipulated to eliminate one variable, allowing for the other variable to be solved.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if two lines are parallel from their equations?

Back

If the slopes of the lines are equal, the lines are parallel.

Front

What is the slope-intercept form of a linear equation?

Back

The form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and write them together.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x=0.

Front

What does it mean for two lines to be skew?

Back

Skew lines are lines that do not intersect and are not parallel, existing in different planes.