Question

find the integers that satisfy each of the following equations. 1. | x | =5 2. - | y | = -6 3. - | b | = -8 4. | a | = 45 5. 26 = | y |

Answer 1

Answer:

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Step-by-step explanation:

5x−7y=3 ......(i)

⇒x−

5

7y

=

5

3

⇒x−y−

5

2y

−

5

3

=0

⇒x−y−

5

2y+3

=0

We are solving for positive integers, so x and y are integers

5

2y+3

= integer

Multiplying by 3, we get

⇒

5

6y+9

= integer

⇒y+1+

5

y+4

= integer

Let the integer be p

5

y+4

=p

⇒y=5p−4 ......(ii)

Substituting in (i), we eget

5x−7(5p−4)=3

⇒5x=35p−25

⇒x=7p−5 .....(ii)

We see from (ii) that y<0 for integer p<1

So, the minimum value of p is 1

Substituting p in (ii) and (iii)

⇒y=1,x=2

So, the least value of x is 2 and y is 1.