Question

How do you write a system of equations that will have (3,2) as a solution?

Answer 1

There are many pairs of equations that have `(3,2)` as a solution.

Probably the simplest pair is
`x=3`
`y=2`

A less trivial pair of linear equations could be generated using the slope-point formula for a straight line:
`(y-2)/(x-3) = m` where `m` is an arbitrary slope
By picking two different values for `m` (say `2` and `5`)
we would have
`(y-2)/(x-3) = 2`
`rarr y = 2x -4`
and
`(y-2)/(x-3) = 5`
`rarr y = 5x -13`

If you want one of the equations to be non-linear, for example a quadratic of the form
`y = x^2-7x+c` for some constant value `c`
simply plug in `(3,2)` for `(x,y)` to solve for `c`
`rarr c =14`
so
`y=x^2-7x+14`
combined with any one of the previous (linear) equations would have a solution of `(3,2)` (although it might not be the only solution).