To solve the system of linear equations:

\[
3x - 8y = 19
\]
\[
3x + 5y = -46
\]

we can use either elimination or substitution. Here, I'll proceed with elimination to remove \(x\) from the equations.

1. **Subtract the two equations**:

   \[
   (3x - 8y) - (3x + 5y) = 19 - (-46)
   \]

   Simplify the equation:

   \[
   3x - 8y - 3x - 5y = 65
   \]
   \[
   -13y = 65
   \]

2. **Solve for \(y\)**:

   \[
   y = \frac{65}{-13} = -5
   \]

3. **Substitute \(y = -5\) back into one of the original equations**. Using the first equation:

   \[
   3x - 8(-5) = 19
   \]
   \[
   3x + 40 = 19
   \]
   \[
   3x = 19 - 40
   \]
   \[
   3x = -21
   \]
   \[
   x = \frac{-21}{3} = -7
   \]

Thus, the solution to the system is:

\[
x = -7, \quad y = -5
\]

Would you like further clarification on any steps?

Here are related questions you might find interesting:
1. How does the elimination method differ from substitution?
2. Can systems of equations have no solution or infinitely many solutions?
3. What are some practical applications of solving linear systems?
4. How would the solution change if both equations had different coefficients?
5. What strategies exist for solving nonlinear systems of equations?

**Tip:** Always double-check your solution by substituting the values back into the original equations to verify correctness.

Explore how to solve the system of linear equations 3x - 8y = 19 and 3x + 5y = -46 using the elimination method. This solution includes a step-by-step approach to finding values for x and y, 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