https://r2.erweima.ai/mathbot/image/17266255799170gfar59h.jpg

The image contains a set of systems of linear equations to be solved using the method of substitution. Let's break them down step by step and solve them.

### a) 
\[
\left\{
\begin{aligned}
y &= x + 15 \\
2y &= 3x - 12
\end{aligned}
\right.
\]

**Step 1:** Substitute \( y = x + 15 \) from the first equation into the second equation:
\[
2(x + 15) = 3x - 12
\]

**Step 2:** Expand and simplify:
\[
2x + 30 = 3x - 12
\]
\[
30 + 12 = 3x - 2x
\]
\[
x = 42
\]

**Step 3:** Substitute \( x = 42 \) back into \( y = x + 15 \):
\[
y = 42 + 15 = 57
\]

**Solution for a:** \( x = 42, y = 57 \)

---

### b)
\[
\left\{
\begin{aligned}
y &= 4x \\
5x + 2y &= 26
\end{aligned}
\right.
\]

**Step 1:** Substitute \( y = 4x \) into the second equation:
\[
5x + 2(4x) = 26
\]

**Step 2:** Simplify:
\[
5x + 8x = 26
\]
\[
13x = 26 \implies x = 2
\]

**Step 3:** Substitute \( x = 2 \) into \( y = 4x \):
\[
y = 4(2) = 8
\]

**Solution for b:** \( x = 2, y = 8 \)

---

Let me know if you'd like to go over the other parts in more detail. Would you like to continue with the other equations or have any specific ones you want to focus on?

Here are 5 questions to expand on what we've covered:

1. How does the substitution method differ from the elimination method in solving systems of equations?
2. What would happen if the system of equations had no solution?
3. Can you solve systems of linear equations graphically, and how does that relate to substitution?
4. What is the significance of linear systems with infinite solutions?
5. How can we check if a system of equations is inconsistent before solving?

**Tip:** After solving a system of equations, it's always good practice to substitute your solution back into the original equations to verify the results.

Solve each system of equations using the substitution method.

Learn how to solve systems of linear equations using the substitution method. This exercise involves finding the solutions for various systems by substituting one equation into another, simplifying, and solving step-by-step. Suitable for students in Grades 8-10.

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