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

1 Answer
Mar 28, 2015

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).