Intro to Systems of Equations- Algebra 2

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 when a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean when a system of equations has infinitely many solutions?

Back

The equations represent the same line, so every point on the line is a solution.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is a linear-quadratic system?

Back

A system that consists of one linear equation and one quadratic equation.

Front

How do you solve a linear-quadratic system?

Back

By substituting the linear equation into the quadratic equation or vice versa.

Front

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

Back

It represents the solution(s) to the system.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.