https://file.aiquickdraw.com/mathbot/file/1729523726146wexg915b.jpg

Let's solve the system of equations by substitution. The system is:

\[
-7x - 2y = -38
\]
\[
-3y = x
\]

### Step 1: Express \(x\) in terms of \(y\)
From the second equation, we already have \(x = -3y\).

### Step 2: Substitute \(x = -3y\) into the first equation

Substitute \(x = -3y\) into the first equation \(-7x - 2y = -38\):

\[
-7(-3y) - 2y = -38
\]

Simplify the expression:

\[
21y - 2y = -38
\]

\[
19y = -38
\]

### Step 3: Solve for \(y\)

Divide both sides by 19:

\[
y = \frac{-38}{19} = -2
\]

### Step 4: Substitute \(y = -2\) into \(x = -3y\)

Now, substitute \(y = -2\) into \(x = -3y\):

\[
x = -3(-2) = 6
\]

### Solution:

The solution to the system is \(x = 6\) and \(y = -2\), or \((6, -2)\).

Would you like further details or explanations on any step?

---

Here are some related questions to deepen your understanding:

1. How do you graphically interpret the solution of a system of linear equations?
2. What is the method of substitution, and when is it preferable over elimination?
3. How would the solution change if the second equation was \(3y = x\) instead of \(-3y = x\)?
4. What is the significance of having one solution, infinitely many solutions, or no solutions in a system of equations?
5. How can you check if the solution \((6, -2)\) satisfies both equations?

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

Solve the system by substitution.
-7x - 2y = -38
-3y = x

Learn how to solve a system of linear equations using the substitution method. This step-by-step guide tackles the equations -7x - 2y = -38 and -3y = x, leading to the solution (6, -2). Perfect for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation