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 solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

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

Back

A consistent system has at least one solution, where the graphs of the equations intersect.

Front

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

Back

An inconsistent system has no solutions, meaning the graphs of the equations do not 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 plane that satisfies 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 write an inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols.

Front

What does it mean to shade above or below a line in graphing inequalities?

Back

Shading above the line indicates solutions where y is greater than the line, while shading below indicates solutions where y is less than the line.

Front

How can you represent a word problem involving money with a system of equations?

Back

Define variables for the unknowns, write equations based on the relationships described in the problem, and solve the system.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where the values satisfy all equations simultaneously.