Question

3 (x + y) = y

If (x,y) is a solution to the equation above and y ≠ 0, what is the ratio of x/y

Answer 1

x/ y = -2/ 3

Step-by-step explanation:

we have:

3(x + y) = y

distributing 3 within the parenthesis:

=> 3x + 3y = y

taking y to the other side, changing its sign in the process

=> 3x = y - 3y

=> 3x = y(1 - 3)

=> 3x = -2y

you can represent any integer as a fraction by putting a "1" in the denominator

`\implies \mathsf{ (3x)/(1) = - (2y)/(1) }`

taking y to the denominator on the LHS and 3 to the denominator on the RHS

`\implies \mathsf{ (x)/(y) = - (2)/(3) }`

that makes the ratio, x/y = -2/ 3

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Hope this helps!

Answer 2

`\\ \sf\Rrightarrow 3(x+y)=y`

• Use distributive law

`\\ \sf\Rrightarrow 3x+3y=y`

• Take y to right

`\\ \sf\Rrightarrow 3x=y-3y`

• Take y common

`\\ \sf\Rrightarrow 3x=-2y`

`\\ \sf\Rrightarrow (x)/(y)=(-2)/(3)`

`\\ \sf\Rrightarrow x:y=-2:3`