Use the method of substitution to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.

{5x−y=32x=−34

We are given the following system of equations:

1. \( 5x - y = 3 \)
2. \( 2x = -34 \)

### Step 1: Solve one equation for one variable.
Let's start by solving the second equation for \( x \):

\[
2x = -34
\]

Divide both sides by 2:

\[
x = \frac{-34}{2} = -17
\]

### Step 2: Substitute the value of \( x \) into the first equation.
Now substitute \( x = -17 \) into the first equation \( 5x - y = 3 \):

\[
5(-17) - y = 3
\]

Simplify:

\[
-85 - y = 3
\]

### Step 3: Solve for \( y \).
Add 85 to both sides:

\[
-y = 3 + 85
\]

\[
-y = 88
\]

Multiply both sides by -1:

\[
y = -88
\]

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

\[
x = -17, \quad y = -88
\]

### Conclusion:
The system is independent, and the unique solution is \( (-17, -88) \).

---

Do you want more details on any part of the process? Here are 5 related questions to deepen your understanding:

1. How can we verify if the system is dependent or independent?
2. What happens if the system has no solution?
3. How do you solve systems of equations with fractions?
4. Can we solve the system using the elimination method instead?
5. How can you apply the substitution method to non-linear systems?

**Tip:** Always substitute carefully to avoid errors and verify by plugging the solution back into both original equations!

Use the method of substitution to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.

{5x−y=3, 2x=−34}

Learn how to solve the system of equations 5x−y=3 and 2x=−34 using the substitution method. This problem demonstrates key algebraic concepts, including solving systems of linear equations and verifying the uniqueness of solutions. Suitable for students in Grades 8-10.

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