What is the solution to this system of equations? 
2/3x+y=6, -2/3x-y=2,
(1, )

(0, 8)

infinitely many solutions

no solution

To determine the solution to the system of equations, we will add the two equations together to eliminate one of the variables. 

The system of equations is:

\[
\frac{2}{3}x + y = 6
\]
\[
-\frac{2}{3}x - y = 2
\]

Let's add the two equations:

\[
\left(\frac{2}{3}x + y\right) + \left(-\frac{2}{3}x - y\right) = 6 + 2
\]

Simplifying the left side:

\[
\frac{2}{3}x - \frac{2}{3}x + y - y = 8
\]

This simplifies to:

\[
0 = 8
\]

This is a contradiction, which means the system of equations has **no solution**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What does it mean for a system of linear equations to have no solution?
2. How can you determine if a system of equations has infinitely many solutions?
3. What are the possible outcomes when solving a system of linear equations?
4. How can you solve a system of linear equations using the substitution method?
5. What are some real-life applications of solving systems of linear equations?

**Tip:** When adding or subtracting equations in a system, if you end up with a false statement like \( 0 = 8 \), this indicates that the system has no solution, meaning the lines are parallel and never intersect.

Understand the solution to the system of equations 2/3x + y = 6 and -2/3x - y = 2. Learn why this system has no solution and explore the mathematical reasoning behind it. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation