INTRO Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations 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 graphing the equations and observing the intersection points.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate where the line crosses the y-axis.