To solve the given problem, we start by equating the vectors on both sides of the equation:

This equation can be split into component equations:

We will solve this system of equations step-by-step.
Step 1: Solve for from equation (2):

Step 2: Substitute into equations (1) and (3):

From equation (1):

(Equation A)
From equation (3):

Step 3: Solve equations and simultaneously:

Multiply equation by 5 and equation by 8 to eliminate :

Subtract equation from equation :

Substitute back into equation :

Finally, substitute and into the expression for :

Therefore, the solution to the system of equations is .
Comparing with the given options, we see that the closest match is option :

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