https://file.aiquickdraw.com/mathbot/file/1728195242130jfe1ujw0.jpg

The system of equations in your image is:

\[
1. \quad x + y = 4.25
\]
\[
2. \quad 16.90x + 4y = 36.35
\]

We can solve this system using the **substitution method**. Here's the step-by-step process:

### Step 1: Solve the first equation for one variable
From equation (1), solve for \( y \):

\[
x + y = 4.25 \quad \Rightarrow \quad y = 4.25 - x
\]

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

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

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

\[
16.90x + 4(4.25) - 4x = 36.35
\]
\[
16.90x + 17 - 4x = 36.35
\]
\[
(16.90x - 4x) = 36.35 - 17
\]
\[
12.90x = 19.35
\]

Now, solve for \( x \):

\[
x = \frac{19.35}{12.90} \quad \Rightarrow \quad x = 1.5
\]

### Step 4: Solve for \( y \)
Now that we know \( x = 1.5 \), substitute this back into the expression for \( y \) from Step 1:

\[
y = 4.25 - 1.5 = 2.75
\]

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

Would you like to see the graphical solution or further explanation on graphing? Feel free to ask any questions!

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Here are 5 relative questions:
1. How would you graph these two equations?
2. Can you solve the system using the elimination method instead of substitution?
3. What happens if you multiply the first equation by a scalar before solving?
4. How do you check the solution for consistency in both equations?
5. What are the different methods for solving systems of linear equations?

**Tip:** Always substitute your solution back into both original equations to verify that it's correct.

Solve the system of equations using substitution and graphing.

Learn how to solve the system of linear equations x + y = 4.25 and 16.90x + 4y = 36.35 using the substitution method. A step-by-step guide is provided, including explanations of the substitution method and graphing. This topic is suitable for high school students in Grades 9-12.

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