Question

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Answer 1

Answer:

Given equation is 4x + 3y =12

On putting x = 0 in Eq. (i), we get

4(0) +3y =12 ⇒ 3y =12

⇒ y = 12 / 3 = 4

So, (0, 4) is a solution of given equation.

On putting y = 0 in Eq. (i), we get

4x+ 3 (0) =12 ⇒ 4x =12

x = 12 / 4 =3

So, (3, 0) is a solution of given equation.

On putting x =1 in Eq. (i), we get

4(1) + 3y=12 ⇒ 3y = 12 - 4 = 8 ⇒ y = 8 / 3

So, (1,8 / 3) is another solution of the given equation.

Further, putting x = 2 in Eq. (i), we get

4(2) + 3y = 12 ⇒ 3y = 12 - 8 = 4 ⇒ y = 4 / 3

So, (2, 4 / 3) is also a solution of the given equation.

Hence the four solutions of given equation are (0, 4), (3, 0), (1, 8 / 3) and (2,4 / 3).

Answer 2

Mathematics includes the study of such topics as quantity, structure, space, and change. It has no generally accepted definition. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof.