The sum of the original two numbers must be?

Question

I  am thinking of two numbers. If I multiply the first by 4 and the second by 3, the sum of the answers is 109. And if I multiply the first by 3 and the second by 4 and add the results, I get 101. The sum of the original two numbers must be?

Answer 1

4x+3y=109

3x+4y=101

 

try multiplying the first equation by 3 and the second by 4

 

12x+9y=327
12x+16y=404

 

Subtract the first from the second 

 

7y=77

y=11

 

put this value for y into the first equation 

 

 

4x+3(11)=109

4x=109-33

4x=76

x=19

 

4(19)+3(11)=109
3(19)+4(11)=101