Systems of Equations & Inequalities Test Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for an inequality to be represented by a dashed line on a graph?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does the shading in a graph of an inequality represent?

Back

The shading indicates the region of the graph that satisfies the inequality.

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.

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

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 graph a linear inequality?

Back

First, graph the corresponding linear equation as a solid or dashed line, then shade the appropriate region based on the inequality.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied.

Front

How can you represent a real-world situation using a system of equations?

Back

By defining variables for the quantities involved and writing equations based on relationships described in the situation.