Let us solve this system by substitution.
-3x + 8y = 5
6x - 2y = 10
According to equation 2,
6x - 2y = 10
6x = 10 + 2y
thus, x = 10 + 2y / 6
substituting the value of x in equation 1,
-3 ( 10 + 2y / 6) + 8y = 5
-30 - 6y + 8y = 5 x 6 = 30
-30 + 2y = 30
2y = 60
Thus, y = 30.
Substituting the value of y in equation 2,
6x - 2y = 10
6x - 2(30) = 10
6x - 60 = 10
6x = 70.
Thus, x = 70/6.
Thus, x = 70 / 6 ( and y = 30)