Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

No solution occurs when the graphs of the equations are parallel and never intersect.

Front

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

Back

You can determine the solution by finding the point(s) where the graphs of the equations intersect.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.

Front

What happens when you graph the same equation multiple times?

Back

Graphing the same equation multiple times results in the same line, indicating infinitely many solutions.

Front

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

Back

The slope-intercept form is 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

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1).