To solve the system of equations given:

2(4x-5)-3(3+4y)=57(6y-1)-(4+3x)=21y-86

Let's simplify the equations:

8x - 10 - 9 - 12y = 5
8x - 12y - 19 = 5
8x - 12y - 19 - 5 = 0
8x - 12y - 24 = 042y - 7 - 4 - 3x = 21y - 86
42y - 11 - 3x = 21y - 86
-3x + 42y - 21y = -86 + 11
-3x + 21y = -75
-3x + 21y + 75 = 0
-3x + 21y + 75 = 0

Now we have the following equations:

8x - 12y - 24 = 0-3x + 21y + 75 = 0

To solve this system of equations, we can either use substitution or elimination method. Let's use elimination:

Multiply equation 1 by 3 and equation 2 by 8 to eliminate x:
3(8x - 12y - 24) = 3(0)
8(-3x + 21y + 75) = 8(0)

Simplifying:
24x - 36y - 72 = 0
-24x + 168y + 600 = 0

Add both equations together:
-36y + 168y - 72 + 600 = 0
132y + 528 = 0
132y = -528
y = -4

Now that we have found the value of y, we can substitute it back into one of the original equations to find x.

Using Equation 1:
8x - 12(-4) - 24 = 0
8x + 48 - 24 = 0
8x + 24 = 0
8x = -24
x = -3

Therefore, the solution to the system of equations is x = -3 and y = -4.