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 two lines to intersect on a graph?

Back

It means that the system of equations has one unique solution, which is the point of intersection.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if two lines are parallel?

Back

The system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines are the same line?

Back

The system of equations has infinitely many solutions, as every point on the line is a solution.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

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 a line crosses the y-axis, represented as (0, y).

Front

How do you find the y-intercept of an equation?

Back

Set x to 0 in the equation and solve for y.