Systems: Number of Solutions

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the meaning of 'infinitely many solutions' in a system of equations?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as 'rise over run'.

Front

If two lines have the same slope but different y-intercepts, how many solutions does the system have?

Back

No solution, because the lines are parallel.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

Front

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

Back

The lines intersect at a single point, indicating a unique solution.

Front

How do you find the slope from the equation of a line in slope-intercept form?

Back

The slope is the coefficient of x in the equation of the form y = mx + b.

Front

Back

The slope is 2.