Question

if y:3=12y. calculate the positive value of y​

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9th

Maths

Linear Equations in Two Variable

Solution of Linear Equations in Two Variables

Solve 7x + 12y = 220 in pos...

MATHS

Solve 7x+12y=220 in positive integers.

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ANSWER

Given, 7x+12y=220 ........(i)

Dividing by 7, we get

x+

7

12

y=

7

220

⇒x+y+

7

5y

=31+

7

3

⇒x+y+

7

5y−3

=31

We have to solve the equation for positive integers, so x and y are integers which ⇒

7

5y−3

= integer.

Multiplying by 3, we get

7

15y−9

= integer

⇒2y−1+

7

y−2

= integer

⇒

7

y−2

= integer

Let the integer be p.

7

y−2

=p

⇒y=7p+2 .......(ii)

Substituting y in (i),

7x+12(7p+2)=220

⇒7x+84p=196

⇒x=28−12p ......(iii)

So p can take any integral value , but from (iii), we see that x<0 fo p>2 which is not possible as we are solving the equation in positive integers.

So, p can be equal 0,1,2.

Substituting p in (ii), we get

⇒y=2,9,16

Substituting p in (iii), we get

⇒x=28,16,4

So, the solution set is {

x=28,16,4

y=2,9,16