Systems of Equations and Inequalities Test

Front

What is a system of equations?

Back

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

Front

What is a system of inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What does the solution of a system of equations represent?

Back

The point(s) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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.

Front

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

Back

Substitute the point's coordinates into each equation. If it satisfies all equations, it is a solution.

Front

What is the graphical representation of the inequality y ≥ mx + b?

Back

A solid line for y = mx + b, with the region above the line shaded.