How do you solve the simultaneous equations $y+2x=6$ and $y=4/x$ ?

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Answer 1 · 2018-03-09T13:51:14

The solution sets are $(1,4)$ and $(2,2)$

We have $y+2x=6$ and $y=4/x$ . Input the second equation into the first:

$4/x+2x=6$

$(2x^2+4)/x=6$

$2x^2+4=6x$

$2x^2-6x+4=0$

$x^2-3x+2=0$

$x^2-x-2x+2=0$

$x(x-1)-2(x-1)=0$

$(x-1)(x-2)=0$

$x=1,2$

Inputting the first value into equation one:

$y+2*1=6$

$y+2=6$

$y=4$

Inputting the second value into equation one:

$y+2*2=6$

$y+4=6$

$y=2$

The solution sets are $(1,4)$ and $(2,2)$ .

How do you solve the simultaneous equations y+2x=6 y+2x=6 and y=4/xy=4/x?