Table of Contents

- 1 How many solutions x/y z where x/y and z are positive integers?
- 2 How many non negative integer solutions are there of the equation x/y z w 15?
- 3 How many integral solutions will the following equation have P 2 388 Q 2?
- 4 How do you find the number of solutions to x+y+z=10?
- 5 How do you find the total number if x+y+z=10?

## How many solutions x/y z where x/y and z are positive integers?

The number of solutions (x,y,z) of the equation x+y+z=10, where x, y and z are positive integers. 1) (x,y,z) any two can be same integers also. 2) (x,y,z) different integers. What are the different methods by which we can solve this?

**How many solutions x/y z where x/y and z are positive integers does the equation x +y +z 10 have?**

Now if x+y+z=10, then x+y = 10-z, where z can be any integer from 0 to 10. So for any given z there are 10-z+1 = 11-z possibilities for x and y, and the total number of solutions is 11+10+9+… +2+1 = 66. Notice that by “positive” I meant ≥0.

### How many non negative integer solutions are there of the equation x/y z w 15?

Here is my try. Your equation is x+y+z+w=(x+y)+(z+w)=15. First we see x+y and z+w as two unknowns, that is a+b=15 and a,b satisfy 2≤a,b≤13. Easily, we can say that there are 12 positive integer solutions for a and b.

**How many solutions does an integral have?**

Therefore, total number of ways are 14 x 2 x 2 x 3 = 168. Now let two of the variables be equal to 0. In this case, the total number of solutions is equal to 6. Therefore, the total number of integral solutions = 728 + 168 + 6 = 902.

#### How many integral solutions will the following equation have P 2 388 Q 2?

4

Therefore, the number of integral solutions is 4.

**How many solutions x/y 10 have?**

X-y=10 three solutions of linear equation.

## How do you find the number of solutions to x+y+z=10?

(N-1)+1, N+0. Now if x+y+z=10, then x+y = 10-z, where z can be any integer from 0 to 10. So for any given z there are 10-z+1 = 11-z possibilities for x and y, and the total number of solutions is 11+10+9+…+2+1 = 66.

**How many number of integral solutions for is?**

Number of integral solutions for is , So the answer is 402. But, I want to know, How we can find it without using formula. any suggestion !!! The number of solutions of is quite obviously given by Then the number of solutions of can by obtained as Finally, the number of solutions of is (using )

### How do you find the total number if x+y+z=10?

In that case, the total number is finite and can be calculated as follows: The equation x+y=N obviously has N+1 solutions in positive integers, namely 0+N, 1+ (N-1), 2+ (N-2), … (N-1)+1, N+0. Now if x+y+z=10, then x+y = 10-z, where z can be any integer from 0 to 10.

**How many non-negative integral values can be taken with R=3 and N=7?**

Now thus a,b,c can take any non negative integral values as x,y,z could take values only as positive integers. Here r=3 and n=7..substitute the values and the answer comes 36.