(1) To solve the system of linear equations, we can use either substitution or elimination method. Let's use elimination method:

Multiply the second equation by 2:
2(2x + y) = 2(4)
4x + 2y = 8

Now, we can add the two equations together to eliminate the y term:
(3x - 2y) + (4x + 2y) = 7 + 8
7x = 15

Divide both sides by 7 to solve for x:
x = 15/7

Substitute x = 15/7 into the second equation to solve for y:
2(15/7) + y = 4
30/7 + y = 4

To get rid of the fraction, we multiply by 7:
30 + 7y = 28

Subtract 30 from both sides:
7y = -2

Divide both sides by 7 to solve for y:
y = -2/7

Therefore, the solution to the system of linear equations is x = 15/7 and y = -2/7.

(2) To solve the quadratic equation x^2 - x - 6 = 0, we can either factor or use the quadratic formula. Let's use factoring:

We need to find two numbers whose product is -6 and whose sum is -1.
The numbers that satisfy these conditions are -3 and 2:

(x - 3)(x + 2) = 0

Setting each factor equal to zero and solving for x:
x - 3 = 0 or x + 2 = 0

For x - 3 = 0, adding 3 to both sides:
x = 3

For x + 2 = 0, subtracting 2 from both sides:
x = -2

Therefore, the solutions to the quadratic equation x^2 - x - 6 = 0 are x = 3 and x = -2.

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