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. The solution is the point(s) where the equations intersect on a graph.

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they coincide, there are infinitely many solutions.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the boundary line, which represents all the solutions to the inequality.

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 system of inequalities?

Back

Graph each inequality as a line, then shade the appropriate region that satisfies 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, indicating the value of y when x is 0.

Front

How do you solve a word problem involving a system of equations?

Back

Define variables for the unknowns, set up equations based on the problem, and solve the system using substitution or elimination.

Front

What is the meaning of 'at least' in inequalities?

Back

'At least' indicates that the value can be equal to or greater than a certain number.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output.