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

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 graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and connect them with a straight line.

Front

What is the graphical representation of a system of inequalities?

Back

The solution is represented by the shaded region where all inequalities overlap.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What does it mean for two lines to be intersecting in a system of equations?

Back

Intersecting lines have different slopes and will cross at exactly one point, which is the solution to the system.

Front

What is a feasible region in the context of inequalities?

Back

The feasible region is the area on a graph where all constraints (inequalities) are satisfied.

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.