Systems of Equations and Inequalities Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How can you solve a system of equations?

Back

You can solve a system of equations using various methods such as substitution, elimination, or graphing.

Front

What is the substitution method?

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?

Back

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

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the region where the solutions overlap.

Front

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

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

Front

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

Back

An inconsistent system of equations has no solutions, meaning the lines are parallel and never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The graphical representation of a solution to a system of equations is the point(s) where the lines representing the equations intersect.