Unit 5 Inequalities & Systems Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted into them.

Front

How do you determine if a point (x, y) is a solution for the system of equations y = -x + 5 and y = 2x - 7?

Back

Substitute x and y into both equations. If both equations are true, then (x, y) is a solution.

Front

What is the graphical representation of a linear equation?

Back

A linear equation can be represented graphically as a straight line on a coordinate plane.

Front

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

Back

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

Front

How do you find the intersection point of two lines?

Back

To find the intersection point, solve the system of equations formed by the two lines simultaneously.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

Front

What is a system of inequalities?

Back

A system of inequalities consists of two or more inequalities that are considered together.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies all inequalities.

Front

What is the significance of the boundary line in a graph of an inequality?

Back

The boundary line represents the points where the inequality changes from true to false; it is solid for 'greater than or equal to' and 'less than or equal to', and dashed for 'greater than' and 'less than'.