https://file.aiquickdraw.com/mathbot/file/17265513817811dtl1mbr.jpg

We are asked to solve the system of equations using substitution:

\[
\begin{aligned}
3x + 2y &= 19 \\
x &= 3y - 12
\end{aligned}
\]

### Steps for solving by substitution:

1. **Substitute the second equation** \( x = 3y - 12 \) into the first equation:
   \[
   3(3y - 12) + 2y = 19
   \]
   
2. **Simplify the equation**:
   \[
   9y - 36 + 2y = 19
   \]
   Combine like terms:
   \[
   11y - 36 = 19
   \]

3. **Solve for \( y \)**:
   \[
   11y = 19 + 36
   \]
   \[
   11y = 55
   \]
   \[
   y = \frac{55}{11} = 5
   \]

4. **Substitute \( y = 5 \) back into the second equation** to find \( x \):
   \[
   x = 3(5) - 12
   \]
   \[
   x = 15 - 12 = 3
   \]

### Solution:
\[
x = 3, \quad y = 5
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you solve systems of equations using elimination instead of substitution?
2. Can substitution always be used for any system of equations?
3. What are the advantages of substitution over other methods?
4. How would you graphically represent the solution to this system?
5. Can this system be solved by matrix methods like Gaussian elimination?

### Tip:
Always substitute the expression carefully to avoid errors, especially when dealing with negatives or fractions.

Use substitution to solve the system of equations: 3x + 2y = 19 and x = 3y - 12.

Learn how to solve the system of equations 3x + 2y = 19 and x = 3y - 12 using substitution. This detailed step-by-step solution covers algebraic concepts and substitution for solving linear equations. Suitable for students in 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