Answer:
The two numbers are 9 and -26.
The larger number is 9.
Step-by-step explanation:
Let the two unknown numbers be x and y.
The sum of a four times a number x and another number y is 10. Hence:
![4x+y=10](https://tex.z-dn.net/?f=4x%2By%3D10)
And the difference between the two numbers is 35. So:
![x-y=35](https://tex.z-dn.net/?f=x-y%3D35)
So, we have the system of equations:
![\left\{ \begin{array} \ 4x+y=10 \\ x-y=35 \end{array}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%20%5Cbegin%7Barray%7D%20%5C%204x%2By%3D10%20%5C%5C%20x-y%3D35%20%5Cend%7Barray%7D)
From the second equation, we can add y to both sides:
![x=y+35](https://tex.z-dn.net/?f=x%3Dy%2B35)
Now, we can substitute this into the first equation:
![4(y+35)+y=10](https://tex.z-dn.net/?f=4%28y%2B35%29%2By%3D10)
Distribute:
![4y+140+y=10](https://tex.z-dn.net/?f=4y%2B140%2By%3D10)
Simplify:
![5y+140=10](https://tex.z-dn.net/?f=5y%2B140%3D10)
Subtract 140 from both sides:
![5y=-130](https://tex.z-dn.net/?f=5y%3D-130)
Divide both sides by 5:
![y=-26](https://tex.z-dn.net/?f=y%3D-26)
So, the value of y is -26 .
Then it follows that the value of x is:
![x=y+35](https://tex.z-dn.net/?f=x%3Dy%2B35)
Substitute -26 for y:
![x=-26+35=9](https://tex.z-dn.net/?f=x%3D-26%2B35%3D9)
So, our two numbers are 9 and -26.
The larger number is 9.
So, our answer is 9.