Solve the system by substitution.
y, equals, minus, 5, x
y=
−5x
y, equals, minus, 7, x, minus, 14
y=
−7x−14

We are given the following system of equations:

1. \( y = -5x \)
2. \( y = -7x - 14 \)

### Step 1: Substitute the first equation into the second
Since both equations are set equal to \( y \), we can substitute \( y = -5x \) from the first equation into the second equation:

\[
-5x = -7x - 14
\]

### Step 2: Solve for \( x \)
Now, let's solve for \( x \):

\[
-5x + 7x = -14
\]

\[
2x = -14
\]

\[
x = \frac{-14}{2} = -7
\]

### Step 3: Substitute \( x = -7 \) into the first equation to find \( y \)

Now that we know \( x = -7 \), we substitute this value back into the first equation to solve for \( y \):

\[
y = -5(-7) = 35
\]

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

\[
x = -7, \quad y = 35
\]

Would you like a detailed explanation or have any questions? 

Here are 5 related questions for further practice:

1. Solve the system of equations: \( y = 2x + 3 \) and \( y = 4x - 5 \).
2. Solve the system of equations: \( y = 3x - 4 \) and \( y = 5x + 2 \).
3. What happens if both equations in a system are the same? How does it affect the solution?
4. Solve the system of equations using substitution: \( y = 6x + 1 \) and \( y = 2x - 3 \).
5. How can you solve a system of equations using the elimination method instead of substitution?

**Tip:** When solving by substitution, always start by isolating one variable in one of the equations to make substitution easier.

Solve the system by substitution. y = -5x and y = -7x - 14.

Learn how to solve the system of equations y = -5x and y = -7x - 14 using the substitution method. This problem demonstrates key algebraic concepts such as solving linear equations and finding the solution to a system of equations. Ideal for students in Grades 8-10.

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