Question

How can one sixthx _ 5 = one fifthx + 2 be set up as a system of equations?

6y _ x = _30
5y _ x = 10

5y + x = _30
5y + x = 10

6y _ 6x = _30
5y _ 5x = 10

5y + 5x = _30
5y + 5x = 10

Answer 1

6y - x = -30

5y - x = 10

Explanation:

one sixth x - 5 = one fifth x + 2 is equal to (1/6)*x - 5 = (1/5)*x + 2. Isolating x, we get:

(1/6)*x - 5 = (1/5)*x + 2

(1/6)*x - (1/5)*x = 2 + 5

(-1/30)*x = 7

x = -210

Now we want to isolate x from the next system of equations

6y - x = -30 (eq. 1)

5y - x = 10 (eq. 2)

To do so, we follow the next steps. First multiply eq. 2 by 6/5

(6/5)*(5y - x) = (6/5)*10

6y - (6/5)*x = 12 (eq. 3)

Next, subtract eq. 3 to eq. 1

6y - x = -30

-

6y - (6/5)*x = 12

----------------------

- x + (6/5)*x = -30 - 12

(1/5)*x = -42

x = -42*5 = -210

And this is the value of x we wanted to find.

Answer 2

`6y-x=-30`

`5y-x=10`.

Explanation:

Given

`(1)/(6)x-5=(1)/(5)x+2`

Let,
`(1)/(6)x-5=y`

`(x-30)/(6)=y`

By cross multiply we get

`x-30=6y`

By subtraction property of equality

`-30=6y-x`

`6y-x=-30`

Let ,
`(1)/(5)x+2=y`

`(x+10)/(5)=y`

By cross multiply we get

`x+10=5y`

By subtraction property of equality we get

`5y-x=10`

Hence,
`6y-x=-30, 5y-x=10`.