To solve for the value of 11x + 13y, we need to first solve the system of equations:
-9x - 6y = 3 ...(1)
2x + 7y = 6 ...(2)
Multiplying equation (1) by 2, we get:
-18x - 12y = 6 ...(3)
Adding equation (2) and (3), we get:
-16x - 5y = 12
Multiplying this equation by -2, we get:
32x + 10y = -24
Adding this to the original equation (2), we get:
33x = -18
Therefore, x = -18/33
Substituting this value of x in equation (2), we get:
2(-18/33) + 7y = 6
Simplifying, we get:
7y = (396/33) - (198/33) = (198/33)
Therefore, y = (198/33) / 7 = 6/11
Finally, substituting the values of x and y, we get:
11x + 13y = 11(-18/33) + 13(6/11) = -6
So, the value of 11x + 13y is -6.
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