Systems of Linear Equations and Inequalities Review

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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable to solve for the other.

Front

What is the substitution method?

Back

A method of solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality.

Front

What is the solution to the system: 5x + y = 9 and 10x - 7y = -18?

Back

(1, 4) using the elimination method.

Front

What is the solution to the system: y = 2x and x + y = 9?

Back

(3, 6) using the substitution method.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.