Flashcard System of Equations 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 no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

By graphing the equations and identifying the point where the lines intersect.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect.

Front

What does the slope of a line represent?

Back

The rate of change of y with respect to x, indicating how steep the line is.

Front

How do you determine the slope from the equation of a line in slope-intercept form?

Back

The slope is the coefficient of x in the equation y = mx + b.

Front

What is the slope of the line represented by the equation y = 2x - 3?

Back

2

Front

What does it mean if two lines intersect at one point?

Back

The system of equations has exactly one solution.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The two equations represent the same line, meaning they overlap completely.

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, represented by the value of b in y = mx + b.