https://r2.erweima.ai/mathbot/image/17265948629661fmkwmlq.jpg

To solve this system of equations by the method of equalization, we have:

\[
\begin{cases}
3x + y = 10 \\
3x - y = 2
\end{cases}
\]

1. **Step 1: Express \( y \) from both equations:**

   From the first equation:
   \[
   y = 10 - 3x
   \]

   From the second equation:
   \[
   y = 3x - 2
   \]

2. **Step 2: Set the expressions for \( y \) equal to each other:**

   \[
   10 - 3x = 3x - 2
   \]

3. **Step 3: Solve for \( x \):**

   Add \( 3x \) to both sides to get:
   \[
   10 = 6x - 2
   \]

   Add \( 2 \) to both sides to get:
   \[
   12 = 6x
   \]

   Divide by \( 6 \):
   \[
   x = 2
   \]

4. **Step 4: Substitute \( x = 2 \) back into one of the original equations to find \( y \):**

   Substitute into \( 3x + y = 10 \):
   \[
   3(2) + y = 10
   \]
   \[
   6 + y = 10
   \]
   \[
   y = 4
   \]

So, the solution to the system is \( x = 2 \) and \( y = 4 \), which corresponds to option \( \text{b) } \{(2; 4)\} \).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How can you verify if the solution to a system of equations is correct?
2. What is another method to solve this system of equations besides equalization?
3. Can systems of equations have no solutions or infinitely many solutions? Why?
4. How does the graph of a system of equations relate to its solutions?
5. What are some practical applications of systems of linear equations?

**Tip:** Always double-check your solution by substituting it back into the original equations to ensure it satisfies both equations.

Solve the system of equations by equalization: 3x + y = 10, 3x - y = 2. Which of the following is the correct solution? a) (3,1) b) (2,4) c) (-2,16) d) (3,7)

Learn how to solve the system of equations 3x + y = 10 and 3x - y = 2 using the equalization method. This algebra problem explores solving for x and y with a step-by-step approach. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation