System 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

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

Back

An ordered pair is a solution if it satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then use a dashed line for < or > and a solid line for ≤ or ≥. Shade the appropriate region.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates they are not included (< or >).

Front

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

Back

It means 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

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the ordered pair into each equation. If it satisfies all equations, it is a solution.

Front

What is the substitution method for solving a system of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.