Systems of Equations/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 a system of equations to have one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The graphs of the equations are the same line, overlapping completely.

Front

How do you solve a system of equations by substitution?

Back

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

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the appropriate region.