Question

Question #d5b6d

Answer 1

`(5,1)`

`(-11,67/3)`

Explanation:

`4x+3y=23---(1)`

`2x^2-9y=41---(2)`

normally with these we would rearrange one eqn for one variable and substitute into eh other eqn.

Here, however we can quickly eliminate one of the variables as follows

`xx(1)" by " 3`

`12x+9y=69---(1a)`

`2x^2-9y=41---(2)`

ADD

`2x^2+12x=110`

`=>x^2+6x-55=0`

the rearranging is left as an exercise for the reader

`(x+11)(x-5)=0`

`=>x=5" or "x=-11`

`x=5`

using `(1)`

`4xx5+3y=23`

`=>3y=3`

:.y=1#

one soln`(5,1)`

`x=-11`

`4x+3y=23`
-44+3y=23#

`3y=67`

`:.y=67/3`

other soln

`(-11,67/3)`

Answer 2

`x=5,-11`
`y=1,-67/3`

Explanation:

`4x+3y=23`
`3y=-4x+23`
`9y=3(-4x+23)=-12x+69`
Substituting the value of 9y in the second equation,
`2x^2+12x-69=41`
`2x^2+12x-110=0`
`2x^2-10x+22x-110=0`
`2x(x-5)+22(x-5)=0`
`(2x+22)(x-5)=0`
`x=5, -11`
`4x+3y=23`
`3y=-4x+23`
When `x=5`, `3y=-20+23=3` or `y=1`
When `x=-11`, `3y=44+23=67`; `y=67/3`