Systems of Equations and Inequalities

Front

What is a system of equations?

Back

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

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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.

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

Back

It means that the equations represent lines that intersect at exactly one point.

Front

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

Back

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

Front

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

Back

If the lines are parallel, they will have the same slope but different y-intercepts.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations are equivalent, meaning they can be transformed into each other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

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What is the substitution method for solving systems of equations?

Back

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

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What is the elimination method for 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 is the point of intersection in a system of equations?

Back

It is the solution to the system, representing the values of the variables that satisfy all equations.