Types of Solutions from Systems of Equations

Front

What are the types of solutions for a system of equations?

Back

One Solution, No Solution, Infinitely Many Solutions.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

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

Back

The lines representing the equations intersect at exactly one point.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

Back

No solution (the lines are parallel).

Front

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

Back

(1, 3) (the lines intersect at this point).

Front

What is the slope of the line represented by the equation y = 3x + 5?

Back

3 (the coefficient of x).

Front

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

Back

-2 (the coefficient of x).

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

No solution (the lines are parallel).

Front

If two lines have different slopes, what can be said about their solutions?

Back

One solution (the lines intersect at one point).