Question

find three different solutions of 2x+3y=6​

Answer 1

Answer:

Three solutions of the given equation are (0,2), $(1,\frac{4}{3})$ and (3,0).

Step-by-step explanation:

Given the equation

$2x+3y=6$

This is an equation of a straight line. We can give value to $x$ to find corresponding values of $y$ and vice versa.

Put $x=0$ in the equation,

$\implies 2\times 0+3y=6\\\\\implies 3y=6\\\\\implies y= 2$

So one solution of the equation is (0,2).

Now put $x=1$

$\implies 2\times 1+3y=6\\\\\implies 2+3y=6\\\\\implies 3y=6-2=4\\\\\implies y=\dfrac{4}{3}$

Another solution of the equation is $(1,\frac{4}{3})$

Now put $x=3$

$\implies 2\times 3+3y=6\\\\\implies 6+3y=6\\\\\implies 3y=0\\\\\implies y=0$

Hence another solution is (3,0)

So three solutions of the given equation are (0,2), $(1,\frac{4}{3})$ and (3,0).

Also, note that this equation has infinitely many solutions.

Answer 2

Step-by-step explanation:

• take x=1

2(1) + 3y = 6

2 + 3y = 6

Taking 2 to the other side as two is in addition it will get subtracted the other side

3y = 6-2

3y = 4

taking three to the other side as three is in multiplication the other side it will get divided

y = 4/3

• similarly two more solutions can be taken out for example- taking x=3, y= 0 as 0/3 is 0 or taking y=1, x=3/2 etc. , etc.

Hope you understood