Graphing Systems of Inequalities and Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean if two lines intersect on a graph?

Back

It means that the system of equations has one unique solution.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

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 graph the equation y = mx + b?

Back

Start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

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

Back

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

Front

What is the slope of a line?

Back

The slope (m) is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What does it mean for a system of inequalities to be feasible?

Back

It means there is at least one solution that satisfies all inequalities in the system.

Front

How can you identify a solution to a system of inequalities?

Back

A solution is a point that lies within the shaded region of the graph representing the inequalities.