Solve the system by substitution.
minus, 3, x, equals, y
−3x=
y
minus, 9, x, minus, 5, y, equals, minus, 48
−9x−5y=
−48

We are given the system of equations:

1. \(-3x = y\)
2. \(-9x - 5y = -48\)

### Step 1: Substitute the value of \(y\) from the first equation into the second equation

From the first equation, we already know:
\[
y = -3x
\]

Now substitute this into the second equation:

\[
-9x - 5(-3x) = -48
\]

### Step 2: Simplify the second equation

Simplify the terms on the left side:
\[
-9x + 15x = -48
\]

Now combine like terms:
\[
6x = -48
\]

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

Divide both sides by 6:
\[
x = \frac{-48}{6} = -8
\]

### Step 4: Solve for \(y\)

Now that we know \(x = -8\), substitute this value back into the first equation to find \(y\):
\[
y = -3(-8) = 24
\]

### Final Solution:

The solution to the system of equations is:
\[
x = -8, \quad y = 24
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the first equation was \(y = 3x\)?
2. What happens if both equations are multiplied by a common factor before substitution?
3. Can you solve the same system using the elimination method?
4. How would you graph these two equations and find the intersection point?
5. What if the system had no solutions or infinite solutions? How would you identify that?

**Tip:** Always check your solutions by plugging the values of \(x\) and \(y\) back into both original equations.

Solve the system by substitution.
-3x = y
-9x - 5y = -48

Learn how to solve a system of linear equations by substitution with the equations -3x = y and -9x - 5y = -48. This step-by-step solution demonstrates key algebraic concepts, including substitution and combining like terms, suitable for students in Grades 8-10.

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