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 two lines to intersect on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel when graphed?

Back

It means that the system of equations has no solution.

Front

What does it mean if two lines are the same when graphed?

Back

It means that the system of equations has infinitely many solutions.

Front

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

Back

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

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

If a system of equations has one solution, what does the graph look like?

Back

The two lines intersect at exactly one point.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

The lines are parallel and will never intersect.