24-25 - Reflashcard Graphing System of Equations and Inequalities

Front

What is a system of equations?

Back

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

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Front

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

Back

A point is a solution if it satisfies all equations in the system when substituted for the variables.

Front

How do you find the intersection of two lines represented by equations?

Back

Set the equations equal to each other and solve for the variable. Substitute back to find the other variable.

Front

What is the graphical representation of y = mx + b?

Back

It is a straight line where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

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 included (< or >).

Front

How can 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 meaning of the term 'feasible region' in the context of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.

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, indicating the value of y when x = 0.