Number of Solutions to Systems of Equations

Front

What is the number of solutions to a system of equations if the lines are parallel?

Back

No Solution

Front

What is the number of solutions to a system of equations if the lines coincide?

Back

Infinitely Many Solutions

Front

What is the number of solutions to a system of equations if the lines intersect at one point?

Back

One Solution

Front

What does it mean if two equations have the same slope but different y-intercepts?

Back

The system has No Solution (the lines are parallel).

Front

What does it mean if two equations have the same y-intercept but different slopes?

Back

The system has One Solution (the lines intersect at one point).

Front

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

Back

2

Front

What is the slope of a line represented by the equation y = -1/2x + 4?

Back

-1/2

Front

If two equations are the same, what can be said about their solutions?

Back

The system has Infinitely Many Solutions.

Front

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

Back

If the lines are parallel (same slope, different y-intercepts).

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations are identical (same slope and y-intercept).