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We are given the following system of simultaneous equations:

\[
9y + 4x = 15.5 \quad \text{(Equation 1)}
\]
\[
5y + 3x = 9 \quad \text{(Equation 2)}
\]

### Step 1: Solve one of the equations for one variable
We can start by solving Equation (2) for \(x\) in terms of \(y\).

From Equation (2):
\[
5y + 3x = 9
\]
Solve for \(x\):
\[
3x = 9 - 5y
\]
\[
x = \frac{9 - 5y}{3}
\]

### Step 2: Substitute the expression for \(x\) into Equation (1)
Now, substitute \(x = \frac{9 - 5y}{3}\) into Equation (1):

\[
9y + 4\left(\frac{9 - 5y}{3}\right) = 15.5
\]

### Step 3: Simplify and solve for \(y\)
Simplify the equation:
\[
9y + \frac{4(9 - 5y)}{3} = 15.5
\]
\[
9y + \frac{36 - 20y}{3} = 15.5
\]

Multiply through by 3 to eliminate the fraction:
\[
3(9y) + (36 - 20y) = 3(15.5)
\]
\[
27y + 36 - 20y = 46.5
\]
\[
7y + 36 = 46.5
\]
\[
7y = 46.5 - 36
\]
\[
7y = 10.5
\]
\[
y = \frac{10.5}{7} = 1.5
\]

### Step 4: Substitute \(y = 1.5\) back into the expression for \(x\)
Now substitute \(y = 1.5\) into the equation for \(x\):

\[
x = \frac{9 - 5(1.5)}{3}
\]
\[
x = \frac{9 - 7.5}{3}
\]
\[
x = \frac{1.5}{3} = 0.5
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 0.5, \quad y = 1.5
\]

Would you like further details on any part of this solution or any related topic? Here are five related questions to explore further:

1. How do we solve simultaneous equations using substitution versus elimination?
2. What are other methods to solve systems of equations, like graphing?
3. How can we check the solution of a system of equations?
4. Can simultaneous equations have more than one solution? When does this occur?
5. What are some real-life applications of solving simultaneous equations?

**Tip:** Always verify your solution by substituting the values of \(x\) and \(y\) back into the original equations!

Solve these simultaneous equations: 9y + 4x = 15.5 and 5y + 3x = 9

Learn to solve the system of simultaneous equations 9y + 4x = 15.5 and 5y + 3x = 9 using the substitution method. This step-by-step solution is ideal for students in Grades 8-10, covering key algebraic concepts and linear equations.

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