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 if two lines are parallel in a system of equations?

Back

They have no solution because they never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

They have infinitely many solutions because they overlap completely.

Front

What does it mean if two lines intersect at a point in a system of equations?

Back

They have one unique solution, which is the point of intersection.

Front

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

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

What is the slope of the line represented by the equation y = -4x + 2?

Back

The slope is -4.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of the solution (1, -4)?

Back

It is the point where the x-coordinate is 1 and the y-coordinate is -4 on the graph.