Solve the system by substitution.
y, equals, minus, 7, x
y=
−7x
y, equals, 9, x, plus, 32
y=
9x+32

To solve the system of equations by substitution, follow these steps:

### Given Equations:
1. \( y = -7x \)
2. \( y = 9x + 32 \)

### Step 1: Substitute the first equation into the second.
Since \( y \) is equal to \( -7x \), we can substitute \( -7x \) for \( y \) in the second equation:

\[
-7x = 9x + 32
\]

### Step 2: Solve for \( x \).
Now, we'll solve this equation for \( x \).

\[
-7x - 9x = 32
\]

\[
-16x = 32
\]

\[
x = \frac{32}{-16} = -2
\]

### Step 3: Substitute \( x = -2 \) back into the first equation to find \( y \).
Now that we have \( x = -2 \), substitute it back into the first equation \( y = -7x \):

\[
y = -7(-2) = 14
\]

### Solution:
The solution to the system of equations is:

\[
x = -2, \quad y = 14
\]

Would you like more details or have any questions?

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Here are some related questions you might be interested in:
1. How can substitution be used to solve systems of equations with more than two variables?
2. What are the advantages of using substitution over other methods, like elimination?
3. How can you verify the solution of a system of equations?
4. What happens if both equations are equivalent after substitution?
5. How would you solve a system of equations graphically?
6. Can substitution be used for non-linear systems of equations?
7. How does substitution compare to matrix methods in solving systems of equations?
8. What are the potential pitfalls when solving systems by substitution?

**Tip:** Always check your solution by substituting the values of \( x \) and \( y \) back into the original equations to ensure they satisfy both equations.

Learn how to solve a system of equations by substitution method. This problem involves two linear equations: y = -7x and y = 9x + 32. Follow a step-by-step solution to find the values of x and y. Suitable for high school students studying algebra and systems of equations.

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