https://file.aiquickdraw.com/mathbot/file/1729084697753wxhwxxpq.jpg

To solve the system of equations:
\[
x - y = -3
\]
\[
-8x + y = 45
\]

we can use either the substitution method or the elimination method. Here, let's proceed with the substitution method.

### Step 1: Solve the first equation for \( y \).
From \( x - y = -3 \), we can rearrange it to solve for \( y \):
\[
y = x + 3
\]

### Step 2: Substitute \( y = x + 3 \) into the second equation.
Substitute \( y \) in \( -8x + y = 45 \):
\[
-8x + (x + 3) = 45
\]
Combine like terms:
\[
-7x + 3 = 45
\]
Subtract 3 from both sides:
\[
-7x = 42
\]
Divide by -7:
\[
x = -6
\]

### Step 3: Find \( y \) using \( y = x + 3 \).
Substitute \( x = -6 \):
\[
y = -6 + 3 = -3
\]

### Solution
The solution to the system of equations is:
\[
x = -6, \quad y = -3
\]

Would you like further details or have any questions?

### Related Questions:
1. How can we verify that the solution \((x, y) = (-6, -3)\) satisfies both original equations?
2. What would be the graphical interpretation of this solution?
3. How would the solution change if the original equations were multiplied by a constant?
4. Can we use the elimination method to solve this system? How?
5. What if the second equation was \(-8x + y = 40\)? What would be the solution?

### Tip:
Always check your solution by substituting the values back into the original equations to ensure accuracy.

Find the solution of the system of equations:
x - y = -3
-8x + y = 45

Learn how to solve the system of equations x - y = -3 and -8x + y = 45 using the substitution method. This problem covers essential algebraic concepts suitable for Grades 8-10, providing a detailed step-by-step solution.

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