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 a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What does the graph of a system of equations represent?

Back

The graph represents the relationships between the variables and the solutions to the equations.

Front

What is the solution to a system of equations represented graphically?

Back

The point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

What does it mean if two lines overlap in a system of equations?

Back

It means the system has infinitely many solutions because every point on the line is a solution.

Front

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

Back

By plotting both equations on the same graph and identifying the intersection point.

Front

What is the significance of the coordinates of the solution point?

Back

They represent the values of the variables that satisfy both equations.

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).