{-3 x+5 y+6 z=-8 3 x+y+z=-4 x-4 y-2 z=-9.

To solve the system of linear equations, we can use the method of substitution or elimination. Let's use the elimination method to solve this system.First, let's multiply the second equation by 3 to make the coefficients of x in the first and second equations equal: Next, let's add the first and second equations to eliminate x: Now, let's multiply the second equation by 3 to make the coefficients of x in the second and third equations equal: Next, let's add the first and second equations to eliminate x: Now, let's add the two equations to eliminate y: Dividing both sides by 12, we get: Now, let's substitute the value of z into the first equation:\( -3 x+5 y+6(-\frac{47}{12})=-8 \)Simplifying, we get: Multiplying both sides by 2 to eliminate the fraction, we get: Now, let's substitute the value of z into the second equation:\( 3 x+y+(-\frac{47}{12})=-4 \)Simplifying, we get: Multiplying both sides by 12 to eliminate the fraction, we get: Now, we have a system of two equations with two variables: We can solve this system by multiplying the first equation by 6 and the second equation by -1, then adding the two equations to eliminate x: Adding the two equations, we get: Dividing both sides by 48, we get: Now, let's substitute the value of y into the first equation:\( -6 x+10(-\frac{235}{48})-47=-16 \)Simplifying, we get: Multiplying both sides by 24 to eliminate the fraction, we get: Simplifying, we get: Adding 2303 to both sides, we get: Dividing both sides by -144, we get: Therefore, the solution to the system of equations is: