Solve by the linear combination method (with or without multiplication).

6x \-2y = 2
3x + 4y =-5

To solve the given system of equations using the linear combination method, we will eliminate one of the variables by multiplying one or both equations by a suitable number(s) in order to make the coefficients of one of the variables in both equations additive inverses of each other.

Let's start solving the system of equations:
1) Multiply the second equation by 2 to eliminate x:
2(3x + 4y) = 2(-5)
6x + 8y = -10

2) Now, the system of equations becomes:
6x - 2y = 2
6x + 8y = -10

3) Subtract equation 1 from equation 2:
(6x + 8y) - (6x - 2y) = -10 - 2
6x - 6x + 8y + 2y = -12
10y = -12

4) Solve for y by dividing both sides of the equation by 10:
10y/10 = -12/10
y = -6/5

5) Substitute the value of y back into either equation 1 or equation 2 to solve for x. Let's use equation 1:
6x - 2(-6/5) = 2
6x + 12/5 = 2

6) Multiply through by 5 to eliminate the fraction:
5(6x + 12/5) = 5(2)
30x + 12 = 10

7) Simplify the equation:
30x + 12 = 10
30x = 10 - 12
30x = -2

8) Solve for x by dividing both sides of the equation by 30:
30x/30 = -2/30
x = -1/15

Hence, the solution to the system of equations is x = -1/15 and y = -6/5.