Types of Solutions from 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 a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines represented by the equations are the same line.

Front

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

Back

The point where the lines intersect on a graph.

Front

How can you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system of equations y = -x + 2 and y = 3x - 4?

Back

(2, 0)

Front

What does it mean if two lines are intersecting?

Back

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

Front

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

Back

3, which indicates the line rises 3 units for every 1 unit it moves to the right.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

5, which is the point where the line crosses the y-axis.