Math Problem Statement

What is the solution to the system graphed?

Solution

The graph shows two intersecting lines, and the solution to the system of equations is the point where the two lines intersect. To solve this, we need to locate the intersection point on the graph.

From the graph, the two lines intersect at the point (1,2)(-1, 2).

Thus, the correct answer is:

(1,2)\boxed{(-1, 2)}

Would you like further clarification on how to interpret graphs like this or any other details? Here are some related questions that could expand your understanding:

  1. How do you solve systems of equations algebraically instead of graphically?
  2. What are the different methods for solving systems of equations (substitution, elimination)?
  3. How can you identify the slope of a line by just looking at its graph?
  4. Why do some systems of equations have no solutions, one solution, or infinitely many solutions?
  5. What does it mean when two lines on a graph are parallel?

Tip: When solving systems graphically, always check where the lines cross, as that intersection represents the solution (if one exists).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Systems of Equations

Formulas

None (Visual solution by intersection point)

Theorems

Intersection Theorem (The point where two lines intersect is the solution to the system of equations)

Suitable Grade Level

Grades 7-9