https://file.aiquickdraw.com/mathbot/file/1726877992529eehfh29g.jpg

Let's solve this system of linear equations using substitution.

We have the following two equations:

1. \( x = 17 - 4y \)
2. \( y = x - 2 \)

### Step 1: Substitute \( x \) from the first equation into the second equation.

From equation 1: 
\[
x = 17 - 4y
\]
Substitute this into equation 2:
\[
y = (17 - 4y) - 2
\]
Simplify:
\[
y = 17 - 4y - 2
\]
\[
y = 15 - 4y
\]

### Step 2: Solve for \( y \).

Add \( 4y \) to both sides:
\[
y + 4y = 15
\]
\[
5y = 15
\]

Divide both sides by 5:
\[
y = 3
\]

### Step 3: Substitute \( y = 3 \) back into the first equation to solve for \( x \).

From equation 1:
\[
x = 17 - 4y
\]
Substitute \( y = 3 \):
\[
x = 17 - 4(3)
\]
\[
x = 17 - 12
\]
\[
x = 5
\]

### Final Solution:
The solution is \( (x, y) = (5, 3) \).

Would you like further details on any step? Here are some related questions to explore:

1. What is the method of substitution in solving linear systems?
2. How would the solution change if one of the equations were rearranged?
3. What is the graphical interpretation of this solution?
4. Can all linear systems be solved using substitution?
5. How does substitution compare to the elimination method?

**Tip:** When using substitution, always simplify your expressions as much as possible before solving.

Solve the system of linear equations by substitution: x = 17 - 4y and y = x - 2

Learn how to solve the system of linear equations x = 17 - 4y and y = x - 2 using substitution. Follow the step-by-step breakdown of how to substitute and solve for x and y. Suitable for students in Grades 7-10.

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