What is the ordered pairs that satisfy the equation #7x+4y=-6#?

1 Answer
Alan P.
Oct 31, 2015

There is an infinite collection of ordered pairs which satisfy the given equation; a few examples are given in the image below:
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Explanation:

#7x+4y=-6#

#rArr 4y = -7x-6#

#rArr y = -7/4x-6/4#
#color(white)("XXXXXXXXX")-6/4 = -1 1/2# but for hand calculations its probably better to leave it with the same denominator as #-7/4x#

Picking any arbitrary value for #x# lets you calculate the corresponding value for #y# that satisfies the given equation.

Note that if you are looking for integer pairs #(x,y)#
if #x# is an integer multiple of #4# minus #2# (#x in 4n-2, AAninZZ#)
then #y# will also be an integer.

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