Math Problem Statement

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Consider the following graph of a system of equations: What is the solution of the system?

Solution

From the graph you provided, we can see that the two lines intersect at the point where both equations hold true. The solution to the system of equations corresponds to the coordinates of this intersection point.

The blue line and the red line intersect at the point (2,6)(2, 6) on the graph.

Therefore, the solution to the system of equations is:

(2,6)\boxed{(2, 6)}

Would you like to explore how these equations are formed from their respective lines, or do you have any further questions?

Here are 5 questions to expand on this topic:

  1. How can we write the equations of the two lines from the graph?
  2. What methods can we use to solve a system of equations algebraically?
  3. How does graphing help in understanding the solution of a system of equations?
  4. What are the different types of solutions a system of linear equations can have?
  5. How can you verify the solution of a system of equations?

Tip: When solving systems of equations graphically, always double-check the intersection point to ensure the coordinates are correct!

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Math Problem Analysis

Mathematical Concepts

Systems of Equations
Graphing Linear Equations
Intersection Points

Formulas

Equation of a Line: y = mx + b
Intersection of Two Lines

Theorems

The Point of Intersection Theorem

Suitable Grade Level

Grades 8-10