https://file.aiquickdraw.com/mathbot/file/17271766683028jf68odf.jpg

Let's break down and solve the question.

### Part (a)
The equation to solve is:

\[
4a + 3b - 18 = 6a - 11b + 16 = 7
\]

Let's rearrange and simplify each part individually.

#### Step 1: Solve for \(a\) and \(b\) from the given system. 

I'll solve that now.From part (a), we find that \(a = 4\) and \(b = 3\).

### Part (b)
Using these values, we need to solve the following simultaneous equations:

\[
\begin{aligned}
12x + 15y &= 100 \\
-55y + 18x &= -36
\end{aligned}
\]

Let's solve this system of equations next.From part (b), the solutions to the simultaneous equations are:

\[
x = \frac{16}{3}, \quad y = \frac{12}{5}
\]

Would you like a detailed breakdown of any step? Here are some related questions you could explore:

1. How do you solve systems of linear equations using substitution?
2. Can we solve systems of equations graphically?
3. What are other methods for solving simultaneous equations?
4. How do you verify solutions for simultaneous equations?
5. How can we solve a system of equations using matrices?

**Tip:** When solving systems of equations, ensure that both equations are correctly simplified before applying any method (substitution, elimination, etc.).

Solve 4a + 3b - 18 = 6a - 11b + 16 = 7. Using the result of (a), solve the following pairs of simultaneous equations: 12x + 15y = 100, -55y + 18x = -36.

This math problem requires solving a system of linear equations. It involves using results from the first equation to solve simultaneous equations. Suitable for high school students.

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