Flashcard 4.1 to 4.4: Solving Systems

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 if two lines are parallel when graphing a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you represent a linear equation in slope-intercept form?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = 4x - 10?

Back

The slope is 4.

Front

What is the y-intercept of the equation y = 3x - 5?

Back

The y-intercept is -5.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the values of the ordered pair into both equations; if both equations are true, it is a solution.

Front

What is a nonlinear system of equations?

Back

A system that includes at least one equation that is not linear, such as quadratic or exponential equations.

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 setup fee in the context of the shirt ordering problem?

Back

A fixed cost that must be paid regardless of the number of shirts ordered.