Systems 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 point to be a solution of a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How can you determine if a point (x, y) is a solution to a system of equations?

Back

Substitute x and y into each equation; if all equations are true, then it is a solution.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

What does the graph of an inequality represent?

Back

It represents all the solutions that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a dashed line and does not include the line, while 'y ≤ mx + b' includes the line.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Parallel lines have no solutions because they never intersect.