Solving Systems of Equations 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 for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

How can you determine the solution of a system of equations by graphing?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.

Front

What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other without ever meeting, indicating no solution.

Front

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

Back

(1, 3) - The point where the two lines intersect.

Front

What is the slope of a line in the equation y = mx + b?

Back

The coefficient 'm' represents the slope, indicating the steepness and direction of the line.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.