https://file.aiquickdraw.com/mathbot/file/1726683246986ykcxtgnb.jpg

The image contains two equations that need to be solved for \( X \) and \( Y \).

### First equation:
\[
4 \cdot (3 - 2) = 4 \cdot X - 4 \cdot Y
\]
Simplifying the left-hand side:
\[
4 \cdot 1 = 4 \cdot X - 4 \cdot Y \implies 4 = 4X - 4Y
\]
Dividing the entire equation by 4:
\[
1 = X - Y \implies X = Y + 1
\]
So, \( X = Y + 1 \).

### Second equation:
\[
5 \cdot (X + Y) = 5 \cdot 2 + 5 \cdot 3
\]
Simplifying the right-hand side:
\[
5 \cdot (X + Y) = 10 + 15 \implies 5 \cdot (X + Y) = 25
\]
Dividing both sides by 5:
\[
X + Y = 5
\]

### Solving the system of equations:

We now have two equations:
1. \( X = Y + 1 \)
2. \( X + Y = 5 \)

Substitute \( X = Y + 1 \) into the second equation:
\[
(Y + 1) + Y = 5
\]
\[
2Y + 1 = 5
\]
Subtract 1 from both sides:
\[
2Y = 4
\]
Dividing by 2:
\[
Y = 2
\]
Now substitute \( Y = 2 \) into \( X = Y + 1 \):
\[
X = 2 + 1 = 3
\]

### Final values:
\[
X = 3, \quad Y = 2
\]

Would you like further details or have any questions?

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Here are some related questions for you:
1. How can systems of equations be solved using substitution?
2. What happens if both equations lead to the same result?
3. How can you check if the solutions are correct for both equations?
4. How would the solution change if the coefficients were different?
5. What other methods can be used to solve systems of linear equations?

**Tip:** Always substitute your solution back into the original equations to verify its correctness.

Solve the system of equations: 4(3 - 2) = 4X - 4Y and 5(X + Y) = 5(2) + 5(3)

Learn how to solve a system of equations using substitution. The example uses two linear equations involving variables X and Y, demonstrating algebraic techniques suitable for Grades 6-8.

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