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You provided a system of two linear equations:

\[
\begin{cases}
x + y = 4.25 \\
16.90x + 4y = 36.35
\end{cases}
\]

Let's solve this system using substitution or elimination. I'll begin by solving it step by step.

### Step 1: Solve the first equation for \( y \)
From the equation \( x + y = 4.25 \), we can solve for \( y \):

\[
y = 4.25 - x
\]

### Step 2: Substitute into the second equation
Now substitute \( y = 4.25 - x \) into the second equation:

\[
16.90x + 4(4.25 - x) = 36.35
\]

Expanding this:

\[
16.90x + 17 - 4x = 36.35
\]

### Step 3: Simplify and solve for \( x \)
Simplify the equation:

\[
(16.90x - 4x) + 17 = 36.35
\]

\[
12.90x + 17 = 36.35
\]

Subtract 17 from both sides:

\[
12.90x = 19.35
\]

Now divide by 12.90 to solve for \( x \):

\[
x = \frac{19.35}{12.90} \approx 1.5
\]

### Step 4: Solve for \( y \)
Now substitute \( x = 1.5 \) back into the equation \( y = 4.25 - x \):

\[
y = 4.25 - 1.5 = 2.75
\]

### Final Solution
Thus, the solution to the system is:
\[
x = 1.5, \quad y = 2.75
\]

Would you like a further breakdown or explanation?

Here are some related questions for further practice:
1. How do you solve a system of equations using the elimination method?
2. What is the graphical interpretation of this solution?
3. How would the system change if one of the equations was non-linear?
4. What happens if two equations in a system have no solution?
5. Can you solve a system with three variables using similar methods?

**Tip:** Always double-check your substitution to ensure no arithmetic errors in solving systems of equations.

Solve the system of equations: x + y = 4.25 and 16.90x + 4y = 36.35

Learn how to solve the system of linear equations x + y = 4.25 and 16.90x + 4y = 36.35 using substitution. The solution includes step-by-step instructions suitable for students in Grades 9-11, with a focus on core algebraic methods and simplification techniques.

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