Graphing Systems of Equations

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 no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts.

Front

What is the solution to the system of equations y = 2x + 1 and y = 2x - 3?

Back

No solution, as the lines are parallel.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the intersection point.

Front

What is the solution to the system of equations y = x + 2 and y = -x + 4?

Back

(2, 3), as this is the point where the two lines intersect.

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.