Adding Equations in a System: Commonalities in Tables and Graphs

This lesson explores systems of equations, focusing on what they share with their sum. It covers the definition of a system of equations, provides an example, and explains how solutions are found. The lesson discusses the effects of multiplying and adding equations, showing that adding equations creates a new system with the same solution. Graphical representations and intersections are examined, emphasizing that the solution remains consistent. The lesson concludes by reinforcing the concept that adding equations results in a new system with the same solution point.

What is a system of equations?

• A set of equations with different variables

• A single equation with multiple variables

• An equation with no variables

• A set of equations with the same variables

What happens when you multiply a linear equation by a constant?

• The graph remains unchanged

• The equation becomes non-linear

• The equation loses its variables

• The graph of the line changes

What is the result of adding two equations in a linear system?

• A new equation with the same solution

• An equivalent equation with the same graph

• An equation with no solution

• A new equation with a different solution

What is the solution point of a system of equations?

• A point that satisfies only one equation

• A point that satisfies all equations in the system

• A point that lies outside the graph

• A point that changes with each equation

What remains unchanged when a new equation is added to a system by combining original equations?

• The intercepts of the graphs

• The solution point

• The coefficients of the equations

• The number of variables