Solving systems of equations (Graphing & Substitution)

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

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 does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and look for points of intersection.

Front

What is the graphical representation of intersecting lines?

Back

The lines cross at one point, which is the unique solution to the system.

Front

What is the graphical representation of parallel lines?

Back

The lines run alongside each other and never meet, indicating no solution.

Front

What is the graphical representation of the same line?

Back

The lines overlap completely, indicating infinitely many solutions.

Front

Solve using substitution: y = 2x + 1, x + y = 5. What is the solution?

Back

(2, 3)