Math Problem Statement

x+2y=10 , x+2y=8

Solution

The system of equations you provided is:

  1. x+2y=10x + 2y = 10
  2. x+2y=8x + 2y = 8

Now, let's analyze these equations. Subtract the second equation from the first:

(x+2y)(x+2y)=108(x + 2y) - (x + 2y) = 10 - 8

This simplifies to:

0=20 = 2

This is a contradiction, which means there is no solution to this system of equations. The two lines represented by these equations are parallel and do not intersect.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How can we identify parallel lines from a system of equations?
  2. What are the methods to solve systems of equations?
  3. Can two parallel lines ever have a solution in a system of equations?
  4. What is the difference between inconsistent, consistent, and dependent systems of equations?
  5. How would graphing these two equations show that they are parallel?

Tip: Inconsistent systems have no solution because the lines never intersect!

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Inconsistent Systems
Parallel Lines

Formulas

Subtraction of equations: (x + 2y) - (x + 2y) = 10 - 8

Theorems

Inconsistent Systems Theorem (A system is inconsistent if it leads to a contradiction, such as 0 = 2)
Parallel Line Theorem (Two lines are parallel if their slopes are equal and they have different intercepts)

Suitable Grade Level

Grades 8-10