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 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 equations represent the same line, meaning every point on the line is a solution.

Front

What is the definition of a slope in a linear equation?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on a line.

Front

How do you find the slope of the line represented by the equation y = mx + b?

Back

The slope is the coefficient 'm' in the equation.

Front

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

Back

-2

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where intersections represent solutions.

Front

What does it mean if two lines intersect at one point?

Back

The system of equations has exactly one solution.

Front

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

Back

If the lines are parallel and do not intersect.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b.