Systems of Equations

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 a unique solution?

Back

It means there is exactly one ordered pair (x, y) that satisfies all equations in the system.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

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

Back

Substitute the values of the ordered pair into each equation to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does the term 'ordered pair' refer to in the context of systems of equations?

Back

An ordered pair (x, y) represents a point on the coordinate plane, where x is the horizontal value and y is the vertical value.

Front

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

Back

The intersection point represents the solution to the system, where both equations are satisfied.