Question

How do you solve `y= 1/x` and `x+5y=6` using substitution?

Answer 1

`(x,y)=color(green)(""(1,1)) " or " color(green)(""(5,1/5))`

Explanation:

Given
[1]`color(white)("XXX")y=1/x`
[2]`color(white)("XXX")x+5y=6`

Using [1] we can substitute `1/x` for `y` in [2]
[3]`color(white)("XXX")x+5/x=6`

Multiplying both sides by `x`
[4]`color(white)("XXX")x^2+5=6x`

Rearranging into standard quadratic form:
[5]`color(white)("XXX")x^2-6x+5=0`

Factoring
[6]`color(white)("XXX")(x-1)(x-5)=0`

Allowing the two solutions:
`{:(x=1,color(white)("XX"),x=5),(rarr y=1/1=1,,rarr y=1/5):}`