4 times one number plus 3 times the other is 78. 3 times the first number minus 8 times the other is -45. What are the numbers?

the first number is 11 38/41

The second number is 10 4/41

Step-by-step 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