How do you write a system of equations with one solution, a system of equations with no solution and a system of equations with infinitely many solutions?

1 Answer
Mar 28, 2015

Answer for linear systems assuming the student knows about lines, graphing lines and slopes:

(i) For one solution: use two lines that have different slopes.
(ii) For no solutions: use two lines that have the same slope, but different #y# imtercepts
(iii) For infinitely many solutions use two different (looking) equations for the same line:

(i): #y=3x-4# and #y=5x-4#
or #y=5/7x+1# and #y=-2x+9#

(ii) #y=3x-4# and #y=3x+9#

(iii) It's a bit pointless to write these in slope-intercept form:
#y=3x-4# #rarr# #3x-y=4#
#y=3x-4# #rarr# #-3y=-9x+12# #rarr# #9x-3y=12#

So a system is:
#3x-y=4#
#9x-3y=12#

The above is a bit obvious, so I would use:
#6x-2y=8#
#9x-3y=12#