Systems of Equations and Inequalities Flashcard

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 a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

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 linear equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What is a linear inequality?

Back

An inequality that involves a linear expression, such as y < mx + b.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation. 2. Use a dashed line for < or >, and a solid line for ≤ or ≥. 3. Shade the appropriate region.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What is the solution set of a system of inequalities?

Back

The region on the graph where the shaded areas of the inequalities overlap.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

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

Back

It represents the values of the variables that satisfy all equations in the system.