Question

Solve simultaneously..? `x = 3y` and `x = 1/2 (3 + 9y)`

Answer 1

`x = - 3`
`y = - 1`

Explanation:

The two given equations are both equal to `x`.
Therefore they are equal to each other.

`3y = x` and `x=` `1/2` `(3 + 9y)`

`3y` `=` `1/2` `(3 + 9y)`

First solve for y

1) Clear the fraction by multiplying both sides by 2 and letting the denominator cancel.
After you have multiplied and canceled, you will have this:
`6y = 3 + 9y`

2) Subtract `6y` from both sides to get all the `y` terms together
`0 = 3 + 3y`

3) Subtract 3 from both sides to isolate the `3y` term
`- 3 = 3y`

4) Divide both sides by 3 to isolate `y`
`-1 = y` `larr` answer for `y`

Next solve for `x`

Sub in `-1` in the place of `y` in one of the given equations.

`x = 3y`

Replace `y` with `- 1`
`x = (3)(-1)`

Clear the parentheses
`x = - 3` `larr` answer for `x`
........................

Check
Sub in `-1` and `-3` for `y` and `x` in one of the given equations

`x=` `1/2` `(3 + 9y)`

`-3=` `1/2` `(3 + 9(-1))`

Clear the inner parentheses
`-3=` `1/2` `(3 -9)`

Solve inside the parentheses
`-3=` `1/2` `(- 6)`

Clear the parentheses by distributing the `1/2`
`- 3 = - 3`
Check!

Answer 2

`y=-1,x=-3`

Explanation:

`x=3y`-----------(1)
`x=9/2y+3/2`---(2)

`(1)-(2)` `0=-3/2y-3/2`

`:.-3/2y-3/2=0`

`:.-3/2y=3/2`

`:.y=(3/2)/(-3/2)`

`:.y=-1`

substitute `y=-1` in (1)

`:.x=3(-1)`

`:.x=-3`

~~~~~~~~~~~~

check:-

substitute `y=-1` and `x=-3` in (2)

`:.-3=9/2(-1)+3/2`

`:.-3=-4.5+1.5`

`:.-3=-3`