Question

How do you solve `y=4/x` and `y=x-3` using substitution?

Answer 1

`(-1, -4)`
`(4, 1)`

Explanation:

We have two equations
`y=4/x" "`first equation
`y=x-3" "`second equation

Substitute first equation into the second

`y=x-3" "`second equation
`4/x=x-3" "`second equation

Multiply both sides of the equation by x

`x*(4/x)=x(x-3)`

`cancelx*(4/cancelx)=x(x-3)`

`4=x(x-3)`

`4=x^2-3x`

We have a quadratic equation

`x^2-3x-4=0`

We can solve this by factoring method

`x^2-3x-4=0`
`(x+1 )(x-4)=0`

Equate each factor to 0 to find the roots

First factor

`(x+1 )=0`

`x=-1` first root
and `y=-4`

Second factor

`x-4=0`

`x=4` second root
and `y=1`

God bless....I hope the explanation is useful.