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

What does it mean for a system of equations to have one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

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

Back

By analyzing the graphs: no solution (parallel lines), one solution (intersecting lines), or infinitely many solutions (same line).

Front

What is the graphical representation of a linear inequality?

Back

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

Front

What does the slope of a line represent in a system of equations?

Back

The rate of change of the dependent variable with respect to the independent variable.

Front

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

Back

Identify the variables, translate the relationships into equations, and ensure they represent the same situation.

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 is zero.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope but different y-intercepts, resulting in no solutions.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers, and A is non-negative.