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3 years ago

Solve the given linear Diophantine equation. A) 12x+9y=15 B) 8x+10y=17

Mathematics

1 answer:

Nookie1986 [14]3 years ago

5 0

Answer:

A) (x, y) = (2-3n, 4n-1) . . . . for any integer n

B) no solution

Step-by-step explanation:

A) All coefficients have a common factor of 3, so any solution of the reduced equation will be a solution of the given equation. The reduced equation is ...

4x +3y = 5

A graph of the original shows (x, y) = (2, -1) is a solution. Then other solutions will be those values with a multiple of 4 added to y and the same multiple of 3 subtracted from x:

(x, y) = (2 -3n, 4n -1)

B) The left side of the equation is an even number for any integer values of x and y. The right side is an odd number. There can be no solution.

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Write two ratios equivalent to 24 : 9.

notsponge [240]

Answer:

8:3

16:6

Step-by-step explanation:

First, let's check if 9 and 24 have any common factor. If they do have any common ones, we must find the GCF (greatest common factor).

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors both of the numbers share and 1 and 3. To find the GCF, simply compare one of the factors to the other.

1 < 3

Now that we know the GCF, we can divide the two numbers in the ratio 24 : 9 by it (3).

24:9

24/3:9/3

8:3

Now that our ratio is simplified, it's going to be much easier to find more ratios that are equivalent. 8:3 is already one equivalent ratio, but if we multiply each number in the ratio by any other number, we can get a new equivalent ratio. Let's multiply each number in the ratio by 2:

8:3

8 ⋅ 2:3 ⋅ 2

16:6

So, another equivalent ratio to 24:9 (and 8:3) is 16:6.

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beks73 [17]

Answer:

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Step-by-step explanation:

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xeze [42]

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Step-by-step explanation:

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