Solving Systems 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 two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines overlap completely?

Back

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 from a graph?

Back

By identifying the coordinates of the intersection point of the lines.

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

What is the slope of a line?

Back

The rate at which y changes for a change in x, often represented as 'rise over run'.

Front

What is a y-intercept?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.