Solving Linear Systems & Inequalities

Front

What is a solution to a linear inequality?

Back

A solution to a linear inequality is any point (x, y) that makes the inequality true, typically represented in a shaded region on a graph.

Front

What does a dotted line represent in a graph of an inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does a solid line represent in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

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

Back

A point is a solution to a system of inequalities if it lies in the shaded region of all inequalities in the system.

Front

What is the graphical representation of a system of linear equations with infinitely many solutions?

Back

The graphical representation is two lines that overlap completely, meaning every point on the line is a solution.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

What is the solution to the system of equations: y = 4x + 1 and 3x + 2y = 13?

Back

The solution is (1, 5).

Front

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

Back

It means that the lines representing the equations are parallel and never intersect.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the graph that satisfies the inequality.

Front

How can you tell if a point is in the solution set of an inequality?

Back

You can substitute the point's coordinates into the inequality to see if it makes the inequality true.