Graphing Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean to solve a system of linear equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of linear equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same, meaning they overlap completely.

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

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

How do you graph a linear equation?

Back

Identify the y-intercept (b) and use the slope (m) to find another point, then draw a line through these points.

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 = 0.

Front

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

Back

It represents the rate of change of y with respect to x, indicating how steep the line is.