https://file.aiquickdraw.com/mathbot/file/17257888808880nspppos.jpg

The equation given is:

\[
(4, y) = x(2, 3)
\]

This represents a vector equation. The left side is the vector \((4, y)\), and the right side is the vector \(x(2, 3)\). To solve for \(x\) and \(y\), we need to equate the components of the vectors.

1. From the first component:  
   \[ 4 = 2x \]  
   Solving for \(x\):
   \[
   x = \frac{4}{2} = 2
   \]

2. Now that we know \(x = 2\), substitute this value into the second component:  
   \[ y = 3x = 3(2) = 6 \]

Thus, the solution is:
\[
x = 2, \quad y = 6
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions to explore:
1. How would the solution change if the vectors were in three dimensions?
2. Can you generalize this type of problem to a system of equations?
3. How does solving vector equations relate to matrix operations?
4. What happens if we change one of the vector components to a negative number?
5. How can this type of problem be represented geometrically?

**Tip:** When solving vector equations, always match corresponding components on both sides of the equation to form a system of equations.

Learn how to find the values of x and y in the vector equation (4, y) = x(2, 3) with a detailed step-by-step solution. This problem involves algebraic manipulation of vectors and linear equations, suitable for students in Grades 9-10.

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