Solutions to 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 representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, which is the solution.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

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 + 2?

Back

3 (the coefficient of x represents the slope).

Front

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

Back

5 (the constant term represents the y-intercept).