(4, 5y+9) - (6, 2 - 3, 1y) = 7, 2 + 2,8

Let's simplify the equation you provided step by step. Just to clarify, it looks like you have a subtraction involving vectors, which involves subtracting corresponding components.

So, let’s break it down:

You have:

\[ (4, 5y + 9) - (6, 2 - 3, 1y) = (7, 2 + 2, 8) \]

This looks like it should be organized into components:

1. Left Side:
   • Take the components of the first vector: \( (4, 5y + 9) \)
   • Take the components of the second vector \( (6, 2 - 3 \cdot 1y) = (6, 2 - 3y) \)

The subtraction of the vectors would be:

\[ (4, 5y + 9) - (6, 2 - 3y) = (4 - 6, (5y + 9) - (2 - 3y)) \]

Calculating each component:

For the first component: \[ 4 - 6 = -2 \]

For the second component: \[ (5y + 9) - (2 - 3y) = 5y + 9 - 2 + 3y = (5y + 3y) + (9 - 2) = 8y + 7 \]

Thus, the left side simplifies to: \[ (-2, 8y + 7) \]

2. Right Side: \[ (7, 2 + 2, 8) = (7, 2 + 2.8) = (7, 4.8) \]

Now, we must compare the left side to the right side:

So we have:

\[ (-2, 8y + 7) = (7, 4.8) \]

This gives us a system of equations:

1. \(-2 = 7\) (which is false)
2. \(8y + 7 = 4.8\)

Since the first equation does not hold, it indicates something went wrong. However, let’s solve the second equation for \(y\):

From \(8y + 7 = 4.8\):

Subtract 7 from both sides: \[ 8y = 4.8 - 7 = -2.2 \]

Now, divide by 8: \[ y = -\frac{2.2}{8} = -\frac{11}{40} = -0.275 \]

So the only viable solution is: \[ y = -0.275 \]

In conclusion, based on the simplifications done, the only valid part is that \(y = -0.275\), while the equation itself does not actually hold overall.