Systems Solution Types

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

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

Back

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

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate plane, written as (x, y).

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.