CA HW Flashcard 11.1 RETAKE

Front

What is a system of equations?

Back

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

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

Back

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

Front

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

Back

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

Front

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

Back

It means that the equations represent two lines that intersect at a single point.

Front

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

Back

By graphing the equations and observing the number of intersection points.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method of solving systems of equations?

Back

A method that involves graphing each equation on the same set of axes and finding the points of intersection.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.