Solving systems of linear equations and inequalities

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the line, indicating all the solutions.

Front

What does it mean if a system of linear equations has no solution?

Back

The lines are parallel and never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The two equations represent the same line.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all, it's a solution.

Front

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

Back

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

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation has an equal sign, while a linear inequality has <, >, ≤, or ≥.

Front

How can you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the appropriate region.