Math Problem Statement

Which ordered pair represents a solution to both equations?

Solution

To determine which ordered pair represents a solution to both equations, we need to find the intersection of the two lines on the graph. The solution to both equations is the point where the two lines cross.

From the graph:

  • The two lines intersect at the point (8, 4).

Answer:

(8, 4) is the correct ordered pair that satisfies both equations.


Would you like a step-by-step explanation of how to identify the intersection point or solve for it algebraically?

Here are 5 related questions to deepen your understanding:

  1. How can you algebraically solve a system of two linear equations?
  2. What is the graphical method for solving a system of equations?
  3. How do you identify a solution to a system of equations by looking at a graph?
  4. What happens when two lines are parallel in a system of equations?
  5. How do you verify if an ordered pair satisfies a given equation?

Tip:
The intersection of two lines on a graph always represents the solution to a system of linear equations.

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Math Problem Analysis

Mathematical Concepts

Systems of Linear Equations
Graphing Linear Equations
Intersection of Lines

Formulas

No specific formulas used; solution determined graphically

Theorems

The point of intersection of two lines is the solution to a system of linear equations

Suitable Grade Level

Grades 8-10