On e way of finding the solution to the given system is:
• multiply both sides of the first equation by 4:
4 * (3x + 2y) = 4 * (-6)
12x + 8y = -24
• multiply both sides of the second equation by 3:
3 * (4x - 7y) = 3 * (-8)
12x - 21y = -24
• subtract the second obtained polynomial from the first obtained polynomial:
12x + 8y = -24
12x - 21y = -24
0 + 29y = 0 ⇒ y = 0
• replace y by 0 in the first equation to find x:
3x + 2y = -6
3x + 2 * 0 = -6
3x = -6
x = -6/3
x = -2
Therefore, the only solution to this equation is the ordered pair (-2, 0).