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 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

The equations represent the same line, so every point on the line is a solution.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

How can you determine the number of solutions in a system of equations by graphing?

Back

By observing the points of intersection of the lines represented by the equations.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line and can determine if lines are parallel or intersecting.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

Front

How do you graph a linear equation?

Back

By finding two or more points that satisfy the equation and connecting them with a straight line.

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

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

Back

The point where the graphs of the equations meet, representing the solution to the system.