Solving Systems of Equations Flashcard makeup

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 a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

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

Back

By finding the point where the graphs of the equations intersect.

Front

What is substitution 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 you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system of equations: y = 2x + 3 and y = -x + 1?

Back

(−2, −1) is the solution.

Front

How do you check if a solution is correct for a system of equations?

Back

By substituting the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical representation of the solution to a system of equations with one solution?

Back

Two lines that intersect at exactly one point.

Front

What is the graphical representation of the solution to a system of equations with two solutions?

Back

This situation does not occur for linear equations; they can have either one solution, no solution, or infinitely many solutions.