24-25 - Flashcard - Graphing Systems of Eq and Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables, representing a region on a graph where all inequalities are satisfied.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies each inequality. 4. The solution is where the shaded regions overlap.

Front

What does the solution of a system of equations represent?

Back

The point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations in the system.

Front

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

Back

The graphs of the equations are parallel lines, meaning they never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y > mx + b?

Back

A region above the line y = mx + b, with a dashed line indicating that points on the line are not included.

Front

What is the significance of the slope in a linear equation?

Back

The slope (m) indicates the steepness of the line and the direction it goes: positive slope rises, negative slope falls.

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives, then express them as inequalities using variables to represent the quantities involved.