Redo: Systems of equations and inequalities

Front

What is a system of equations?

Back

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

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect represent the solution(s) to the system.

Front

What does it mean for an ordered pair to be a solution of a system of inequalities?

Back

It means that the ordered pair satisfies all inequalities in the system.

Front

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

Back

Substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What is the difference between a system of equations and a system of inequalities?

Back

A system of equations has exact solutions, while a system of inequalities has a range of solutions that satisfy the inequalities.

Front

What is the method of elimination in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does shading a region in a graph of inequalities represent?

Back

It represents all the possible solutions that satisfy the inequalities.

Front

What is the significance of the intersection point in a system of equations?

Back

It represents the unique solution where both equations are satisfied.

Front

How can you check your solution for a system of equations?

Back

Substitute the solution back into both original equations to verify if both are true.