Answer: the first number is 11 38/41
The second number is 10 4/41
Explanation:
Let x represent the first number.
Let y represent the second number.
4 times one number plus 3 times the other is 78. It means that
4x + 3y = 78- - - - - - - - - -1
3 times the first number minus 8 times the other is -45. It means that
3x - 8y = - 45- - - - - - - - - 2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 4. It becomes
12x + 9y = 234
12x - 32y = - 180
Subtracting, it becomes
41y = 414
y = 414/41
y = 10 4/41
Substituting y = 414/41 into equation 1, it becomes
4x + 3 × 414/41 = 78
4x + 1242/41 = 78
4x = 78 - 1242/41
4x = 1956/41
x = 1956/41 × 1/4
x = 1956/164
x = 11 38/41