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

Question

3085 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T13:51:14

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

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

$\frac{4}{x} + 2 x = 6$ $4/x+2x=6$

$\frac{2 x^{2} + 4}{x} = 6$ $(2x^2+4)/x=6$

$2 x^{2} + 4 = 6 x$ $2x^2+4=6x$

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

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

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

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

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

$x = 1, 2$ $x=1,2$

Inputting the first value into equation one:

$y + 2 \cdot 1 = 6$ $y+2*1=6$

$y + 2 = 6$ $y+2=6$

$y = 4$ $y=4$

Inputting the second value into equation one:

$y + 2 \cdot 2 = 6$ $y+2*2=6$

$y + 4 = 6$ $y+4=6$

$y = 2$ $y=2$

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

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