One integer is nine more than two times another integer. If the product of the integers is 18, how do you find the two integers?

1 Answer
May 19, 2018

Answer:

Solutions integers: #color(blue)(-3,-6)#

Explanation:

Let the integers be represented by #a# and #b#.
We are told:
[1]#color(white)("XXX")a=2b+9# (One integer is nine more than two time the other integer)
and
[2]#color(white)("XXX")a xx b = 18# (The product of the integers is 18)

Based on [1], we know we can substitute #(2b+9)# for #a# in [2];
giving
[3]#color(white)("XXX")(2b+9) xx b=18#

Simplifying with the target of writing this as a standard form quadratic:
[5]#color(white)("XXX")2b^2+9b=18#

[6]#color(white)("XXX")2b^2+9b-18=0#

You could use the quadratic formula to solve for #b# or recognize the factoring:
[7]#color(white)("XXX")(2b-3)(b+6)=0#
giving solutions:
#color(white)("XXX")b=3/2# which is not permitted since we are told the values are integers.
or
#color(white)("XXX")b=-6#

If #b=-6# then based on [1]
#color(white)("XXX")a=-3#