Identifying 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 two lines are parallel in a system of equations?

Back

They have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

They have the same slope and the same y-intercept, resulting in infinitely many solutions.

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is represented by 'm' in the equation.

Front

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

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the y-intercept in the equation y = mx + b?

Back

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

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

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

Back

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