SOLVING SYSTEMS OF EQUATIONS-GRAPHS

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

It means the lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means the equations represent the same line, so there are countless points that satisfy both equations.

Front

How can you determine the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the values of the variables that satisfy all equations in the system.

Front

What is the slope of a line in the context of a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves (rise over run).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How do you identify if two lines are parallel?

Back

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