Solve Systems by Graphing

Front

What is a system of equations?

Back

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

Front

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

Back

The lines are parallel and never intersect.

Front

What does it mean if 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 tell if two lines are parallel when graphing?

Back

They have the same slope but different y-intercepts.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

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 find the slope of a line given two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are identical?

Back

They have the same slope and the same y-intercept.