Systems of Equations and Inequalities Review

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

It means that the point satisfies all equations in the system.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

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 (> or <).

Front

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

Back

Substitute the x and y values of the point into each equation to see if they hold true.

Front

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

Back

It means the lines 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.

Front

What is the solution to the system: y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

What is the significance of the inequality symbol in graphing?

Back

It determines whether the line is solid or dashed and which side of the line is shaded.