Question

How do you solve the system of equations algebraically `y=6-x, x=4.5+y`?

Answer 1

`(21/4,3/4)`

Explanation:

We can substitute `y=6-x" into " x=4.5+y`

`rArrx=4.5+(color(red)(6-x))larr" one variable"`

`rArrx=4.5+6-x`

`rArr2x=10.5`

dividing by 2

`rArrx=5.25=21/4`

Substitute this value into y = 6 - x

`x=21/4toy=6-21/4=3/4`

`rArr(21/4,3/4)" is the solution"`

This could also have been solved by substituting

`x=4.5+y" into " y=6-x"`

You may wish to attempt this yourself, as a check.