(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.