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The problem in the image is as follows:

We are given that \( x \) and \( y \) are integers, and the equation is:

\[
9x + 2y - 5 = 16y - x - 10
\]

We need to solve for \( 3y - 2x \).

### Step 1: Simplify the equation

Start by rearranging the terms:

\[
9x + 2y - 5 = 16y - x - 10
\]

Move all terms involving \( x \) and \( y \) to one side, and constants to the other side:

\[
9x + x + 2y - 16y = -10 + 5
\]

This simplifies to:

\[
10x - 14y = -5
\]

### Step 2: Solve for \( x \) and \( y \)

We can simplify the equation further by dividing through by 2:

\[
5x - 7y = -\frac{5}{2}
\]

Since \( x \) and \( y \) are integers, there seems to be a mistake in my simplification because \( \frac{5}{2} \) is not an integer. Let me correct it:

We should instead keep the equation in its current form for checking different integer values of \( x \) and \( y \).

### Solving the final question:
What is \( 3y - 2x \)?

x and y are integers. Given the equation: 9x + 2y - 5 = 16y - x - 10, solve for 3y - 2x.

Learn how to solve the equation 9x + 2y - 5 = 16y - x - 10 for integer values of x and y, and find the value of 3y - 2x. This step-by-step solution covers key algebraic concepts such as rearranging terms and solving linear equations. Suitable for students in Grades 8-10.

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