https://file.aiquickdraw.com/mathbot/file/1729361911824xkfxu06u.jpg

The system of equations provided in the image is:

\[
\begin{cases}
3x + 5y = -19 \\
x - 3y = 17
\end{cases}
\]

We can solve this system using either substitution or elimination. Let's use substitution:

### Step 1: Solve for \( x \) from the second equation.
From \( x - 3y = 17 \), we can solve for \( x \) as:
\[
x = 17 + 3y
\]

### Step 2: Substitute \( x = 17 + 3y \) into the first equation.
Now, substitute this expression for \( x \) into the first equation \( 3x + 5y = -19 \):
\[
3(17 + 3y) + 5y = -19
\]
Expanding the equation:
\[
51 + 9y + 5y = -19
\]
Combine like terms:
\[
51 + 14y = -19
\]
Solve for \( y \):
\[
14y = -19 - 51
\]
\[
14y = -70
\]
\[
y = \frac{-70}{14} = -5
\]

### Step 3: Substitute \( y = -5 \) back into \( x = 17 + 3y \).
\[
x = 17 + 3(-5) = 17 - 15 = 2
\]

### Solution:
The solution to the system is:
\[
x = 2, \quad y = -5
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you check if the solution to a system of equations is correct?
2. What is the elimination method, and how does it compare to substitution?
3. Can a system of equations have more than one solution? Why or why not?
4. What are some applications of solving systems of equations in real life?
5. How can you solve a system of equations using matrix methods like Gaussian elimination?

**Tip:** Always substitute your solution back into both original equations to verify its correctness.

Solve the system of equations: 3x + 5y = -19 and x - 3y = 17

Learn how to solve the system of linear equations 3x + 5y = -19 and x - 3y = 17 using substitution. A step-by-step solution is provided to simplify and solve for x and y, making it 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