What is the ordered pairs that satisfy the equation #3x - 2y = 6#?

1 Answer
Nov 25, 2017

You can find as many ordered pairs as you want.

Here are some:
#(6,6)#
#(2,0)##larr# This is the #x# intercept
#(0,- 3)##larr# This is the #y# intercept
#(-2,-6)#
#(-6,-12)#

Explanation:

You can write this line in slope-intercept form and use that equation to generate as many ordered pairs as you want.

#3x - 2y = 6#
Solve for #y#

1) Subtract #3x# from both sides to isolate the #-2y# term
#-2y = -3x + 6#

2) Divide both sides by #- 2# to isolate #y#
#y = (3x)/(2) - 3#

Now assign various values to #x# and solve for #y# to generate as many ordered pairs as you want.

Hot tip: Since you'll be dividing #3x# by #2#, choose only even numbers for #x#

... #x# .... | ... #y# ... | . .Ordered Pairs
.............|.............|...................................
... #6# ......| .... #6# ...| . . . #(6,6)#
... #2# ......| .... #0# ...| . . . #(2,0)##larr# This is the #x# intercept
... #0# ......|. #-3# ...| . . . (0,⎯ 3)#larr# This is the #y# intercept
# -2# ......|. #-6# ...| . . . #(⎯ 2,⎯ 6)#
# -6# ......|. #-12# .| . . . #(⎯ 6,⎯ 12)#