Review Linear equations & Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if it has no solutions.

Front

What does it mean for a system of equations to be dependent?

Back

A system of equations is dependent if it has infinitely many solutions, meaning the equations represent the same line.

Front

What does it mean for a system of equations to be independent?

Back

A system of equations is independent if it has exactly one solution, meaning the lines intersect at one point.

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical representation of parallel lines?

Back

Parallel lines are lines in a plane that never meet; they have the same slope but different y-intercepts.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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