https://file.aiquickdraw.com/mathbot/file/1733508726336aojml8ec.jpg

The system of equations given in the image is:

\[
\begin{aligned}
y &= 2x + 1 \quad \text{(Equation 1)} \\
5y - 6x &= 13 \quad \text{(Equation 2)}
\end{aligned}
\]

Let’s solve this system of equations using the **substitution method** since \(y\) is already expressed in terms of \(x\) in Equation 1.

---

### Step 1: Substitute \(y = 2x + 1\) into Equation 2

\[
5(2x + 1) - 6x = 13
\]

Simplify:

\[
10x + 5 - 6x = 13
\]

\[
4x + 5 = 13
\]

\[
4x = 8
\]

\[
x = 2
\]

---

### Step 2: Substitute \(x = 2\) into Equation 1 to find \(y\)

\[
y = 2(2) + 1
\]

\[
y = 5
\]

---

### Final Solution:
\[
x = 2, \quad y = 5
\]

This solution satisfies both equations. Let me know if you'd like a detailed verification or have further questions.

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### Related Questions:
1. Can you solve this system graphically to verify the solution?
2. What is the determinant of the coefficient matrix of this system?
3. How would you solve this system using the elimination method?
4. If \(y = 2x + 1\) were replaced with \(y = -x + 1\), how would the solution change?
5. What real-world scenarios could be modeled with this system of equations?

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**Tip:** When solving systems of equations, substitution is often easier when one equation is already solved for a variable.

Solve the system of equations y = 2x + 1 and 5y - 6x = 13.

Explore how to solve the system of linear equations y = 2x + 1 and 5y - 6x = 13 using the substitution method. This detailed solution is ideal for Grades 8-10, covering key algebraic concepts and step-by-step calculations.

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