Question

How do you solve the following system: #8x-3y=3, x+3y=3 #?

Answer 1

This ordered pair is `(2/3, 7/9)` or `(0.bar6, 0.bar7)`.

Explanation:

Use the elimination method, and then substitution to solve. Line up the two equations, one on top of the other:

`8x - 3y = 3`
`color(white)(8)` `x + 3y = 3`

Now add them together, and notice that `y` will be eliminated because `-3y + 3y = 0`:

`8x color(blue)(- 3y) = 3`
`color(white)(8)` `x color(blue)(+ 3y) = 3`

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`color(white)(x)9x color(white)(+ 0y) = 6`

`9x = 6`

`x = 6/9 rarr 2/3`

Now substitute that value for `x` into another equation, and solve for `y`:

`x + 3y = 3`

`2/3 + 3y = 3`

`2 + 3(3)y = 3(3)`

`2 + 9y = 9`

`9y = 7`

`y = 7/9`

So this ordered pair is `(2/3, 7/9)`. As a repeating decimal, the coordinates are `(0.bar6, 0.bar7)`.

Answer 2

Solution: `x= 2/3 and y= 7/9`

Explanation:

`8 x-3 y=3 ; (1) , x +3 y =3; (2)` , adding equation (1)

and equation (2) we get, `9 x = 6 :. x = 6/9 or x= 2/3`

Putting `x=2/3` in equation (2) we get, `2/3 +3 y =3;` or

`3 y =3- 2/3 or 3 y = 7/3 or y = 7/9`

Solution: `x= 2/3 and y= 7/9` [Ans]