Question

5. If x=2-a and y=2+ a is a solution of the equation 3x – 2y+6=0 find the value
of 'a'. Find three more solutions of the resultant equation.​

Answer 1

-6 is the value of a
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Answer 2

Answer :

• a = 8/5

• Three solutions : (0,3) , (-2,0) , (-4,-3)

Solution :

• Finding the value of a :

Here ,

The given equation is : 3x - 2y + 6 = 0

Also ,

It is given that , x=2-a and y=2+a is a solution of the given equation , thus x=2-a and y=2+a must satisfy the given equation .

Now ,

Putting x = 2 - a and y = 2 + a in the given equation , we get ;

=> 3x - 2y + 6 = 0

=> 3(2 - a) - 2(2 + a) + 6 = 0

=> 6 - 3a - 4 - 2a + 6 = 0

=> 8 - 5a = 0

=> 5a = 8

=> a = 8/5

Hence , a = 8/5 .

• Finding three more solutions :

• If x = 0 , then

=> 3•0 - 2y + 6 = 0

=> -2y + 6 = 0

=> 2y = 6

=> y = 6/2

=> y = 3

• If y = 0 , then

=> 3x - 2•0 + 6 = 0

=> 3x + 6 = 0

=> 3x = -6

=> x = -6/3

=> x = -2

• If y = -3 , then

=> 3x - 2•(-3) + 6 = 0

=> 3x + 6 + 6 = 0

=> 3x + 12 = 0

=> 3x = -12

=> x = -12/3

=> x = -4

Hence ,

(0,3) , (-2,0) , (-4,-3) are solutions of the given equation .

[ Note : We can find other solutions of our choice because infinitely many points lies on a straight line . ]