Mathematics, 26.07.2019 21:30 jonallere04

How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?

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Answer from: taee67

Non-negative integers are positive integers or zero.

1. When x_1=0, then there are such possible cases for x_2 and x_3:

$x_2=0,\ x_3=10;$ $x_2=1,\ x_3=9;$ $x_2=2,\ x_3=8;$ $x_2=3,\ x_3=7;$ $x_2=4,\ x_3=6;$ $x_2=5,\ x_3=5;$ $x_2=6,\ x_3=4;$ $x_2=7,\ x_3=3;$ $x_2=8,\ x_3=2;$ $x_2=9,\ x_3=1;$ $x_2=10,\ x_3=0.$

In total 11 solutions for x_1=0.

2. For x_1=1, there are such possible cases for x_2 and x_3:

$x_2=0,\ x_3=9;$ $x_2=1,\ x_3=8;$ $x_2=2,\ x_3=7;$ $x_2=3,\ x_3=6;$ $x_2=4,\ x_3=5;$ $x_2=5,\ x_3=4;$ $x_2=6,\ x_3=3;$ $x_2=7,\ x_3=2;$ $x_2=8,\ x_3=1;$ $x_2=9,\ x_3=0.$

In total 10 solutions for x_1=1.

3. This process gives you

for

- 9 solutions;for x_1=3

- 8 solutions;for x_1=4

- 7 solutions;for x_1=5

- 6 solutions;for x_1=6

- 5 solutions;for x_1=7

- 4 solutions;for x_1=8

- 3 solutions;for x_1=9

- 2 solutions;for x_1=10

- 1 solution.

4. Add all numbers of solutions:

11+10+9+8+7+6+5+4+3+2+1=66.

there are 66 possible solutions (with non-negative integer variables)

Answer from: zoebtharpe

There are total 66 solutions of the equations.

Step-by-step explanation:

We can find the solution by fixing the first value i.e. x_1 at a time and shifting the other two values and keep on doing for all the possible values of x_1

Hence, the possible cases are as follows:

x_1-x_2-x_3

0-10-0 1-9-0 2-8-0 3-0-7 4-0-6 5-0-5 6-0-4

0-0-10 1-0-9 2-0-8 3-7-0 4-6-0 5-5-0 6-4-0

0-1-9 1-1-8 2-1-7 3-1-6 4-1-5 5-1-4 6-1-3

0-9-1 1-8-1 2-7-1 3-6-1 4-5-1 5-4-1 6-3-1

0-2-8 1-2-7 2-3-5 3-2-5 4-2-4 5-2-3 6-2-2

0-8-2 1-7-2 2-4-3 3-5-2 4-4-2 5-3-2

0-3-7 1-3-6 2-3-4 3-3-4 4-3-3

0-7-3 1-6-3 2-2-6 3-4-3

0-4-6 1-4-5 2-6-2

0-6-4 1-5-4

0-5-5

------------------------------------------------------------------------------------------------------------

7-0-3 8-0-2 9-0-1 10-0-0

7-3-0 8-2-0 9-1-0

7-1-2 8-1-1

7-2-1

Answer from: Quest

mental cunning

explanation:

he is often referred to as a man of twists and turns

Answer from: Quest

which expression can be used to convert 80 us dollars (usd) to australian dollars (aud)?

1 usd = 1.0343 aud

1 aud = 0.9668 usd

step-by-step explanation:

sorry just need the points

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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negativ...