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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

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

Back

By observing the intersection points of the graphs: no intersection means no solution, one intersection means one solution, and overlapping lines mean infinitely many solutions.

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

How do you find the intersection point of two lines graphically?

Back

Plot both lines on the same graph and identify the point where they cross.

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The y-coordinate of the point where the line crosses the y-axis.