Question

If 3x - 5y = 11 and 2x + 3y = 5, then what is the ratio of x to y?

Answer 1

-58/7

Explanation:

Alright so this is a system of equations. First we'll solve the system, and then find the ratio afterwards.

`3x-5y = 11\\2x+3y =5\\`

Isolate for y on both.

`2x + 3y = 5\\3y = 5-2x\\y = (5-2x)/(3)`

and

`3x - 5y = 11\\-5y = 11-3x\\y = (11-3x)/(-5)`

Set both equations equal to each other:

`(11-3x)/(-5) = (5-2x)/(3)\\ \\(3(11-3x))/(-5) = 5-2x\\ \\3(11-3x) = -5(5-2x)\\\\33 - 9x = -25 + 10x\\33 = -25 + 19x\\58 = 19x\\(58)/(19) = x`

We've got x, now let's solve for y:

`y = (11-3x)/(-5) = (11-3((58)/(19)) )/(-5)`

Now we got both x and y, and what they equal.

`y = (-7)/(19)\\`

`x = (58)/(19)`

The ratio of x to y, is essentially
`(x)/(y)`. So we will calculate that.

`((58)/(19) )/((-7)/(19) ) = (58)/(19) * (19)/(-7) = (-58)/(7)`