WU: Solving Systems by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the point(s) where the equations intersect.

Front

What does it mean to solve a system by graphing?

Back

Solving a system by graphing involves plotting the equations on a coordinate plane and identifying the point(s) where the graphs intersect, which represent the solution(s) to the system.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes each equation true when substituted into them.

Front

What does the point (3, 19) represent in the context of a graph?

Back

The point (3, 19) represents a specific solution where, for example, both Lisa and Tammy sold 3 items and earned the same amount of money, which is 19.

Front

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

Back

The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy all equations simultaneously.

Front

What is the solution to the system of equations represented by the points (2, 3) and (1, 3)?

Back

The solution to the system is the point where the two lines intersect, which in this case is (1, 3), indicating the values of the variables at that intersection.

Front

What does it mean if two lines are parallel in a graph of a system of equations?

Back

If two lines are parallel, it means that the system of equations has no solution, as the lines will never intersect.

Front

What is the meaning of a negative solution in a system of equations?

Back

A negative solution, such as (1, -1), indicates that one of the variables has a negative value, which can represent a real-world scenario depending on the context.

Front

How can you verify the solution of a system of equations?

Back

You can verify the solution by substituting the values of the solution back into the original equations to check if they hold true.