Math Problem Statement

When graphing the system y = 3x - 2 and y = -2x + 8, what does the intersection point represent?

Solution

The question asks about the interpretation of the intersection point when graphing the system of equations:

  1. y=3x2y = 3x - 2
  2. y=2x+8y = -2x + 8

The intersection point of two lines represents the solution to the system of equations. This is because the intersection point is the set of coordinates (x,y)(x, y) that satisfies both equations simultaneously. Therefore, the correct answer is:

a. The solution to the system.

Let me know if you'd like a step-by-step explanation or further clarification! Here are some related questions:

  1. What is the method to solve a system of equations algebraically?
  2. How do you graph a system of linear equations step by step?
  3. What are the possible outcomes for systems of two linear equations (e.g., one solution, no solution, infinitely many solutions)?
  4. How do you determine if two lines are parallel or perpendicular using their equations?
  5. What does the slope represent in the equation of a line?

Tip: To find the exact solution to a system, you can use substitution or elimination methods if graphing is not precise.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Systems of Equations
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Intersection Point Theorem (solution to a system of linear equations)

Suitable Grade Level

Grades 8-10