Math Problem Statement

Which of the following represents the solution to the graphed equations? (Graph with two lines intersecting at a point)

Solution

To determine which option represents the solution to the graphed equations, we need to identify the point of intersection of the two lines shown in the graph. The solution to a system of equations is the point where both lines meet.

Steps:

  1. Observe the graph and locate where the two lines intersect.
  2. Note the coordinates (x, y) of the intersection point.

From the image:

  • The lines intersect at the point (6,25)(6, 25).

Thus, the correct answer is:

6, 25

Do you want more detailed explanations about graphing systems of equations or how to solve them algebraically? Let me know!

Here are 5 related questions:

  1. What is a system of linear equations, and how do we graphically solve it?
  2. How do we algebraically find the intersection point of two linear equations?
  3. What is the significance of the slope and y-intercept in linear equations?
  4. Can two lines never intersect? What does that imply about the system of equations?
  5. How do we verify the solution to a system of equations?

Tip: Always double-check the axes and their scales when reading graphs to avoid misinterpreting coordinates.

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Math Problem Analysis

Mathematical Concepts

Graphing Linear Equations
Intersection of Lines
Systems of Equations

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

A system of linear equations has a solution at the point where the lines intersect.

Suitable Grade Level

Grades 6-8