If four times a first number is decreased by three times the second number, the result is zero. The sum of the numbers is -7. Find the numbers?

2 Answers
Apr 16, 2017

Answer:

#-3, and, -4.#

Explanation:

By what is given,

#4N_1-3N_2=0...(1), and, N_1+N_2=-7...(2).#

#(2) rArr 3(N_1+N_2)=-21, i.e., 3N_1+3N_2=-21...(2').#

#(1)+(2') rArr 4N_1+3N_1=0+(-21),#

# rArr 7N_1=-21 rArr N_1=-21/7=-3," &, by (2), then, "N_2=-4.#

Apr 16, 2017

Answer:

#-3# and #-4#

Explanation:

Let's say the first number is #x# and the second number is #y#

So, first we're told that #4*x-3*y=0# and then, that #x+y=-7#

Let's use substitiution!

Our first job is to set #x+y=-7# to #x#:
#x+y=-7#
subtract #y# on both sides
#x=-7-y#

Now, substitute #x# for #(-7-y)# in the firstequation:
#4x-3y=0#
#4(-7-y)-3y=0#
distribute the #4#
#-28-4y-3y=0#
add #28# on both sides
#-4y-3y=28#
combine like-terms
#-7y=28#.
divide by #-7# on both sides
#y=-4#

Now that we know #y=-4#, we can solve for #x#:
#x+y=-7#
#x+(-4)=-7#
add #4# on both sides
#x=-3#

Just to double-check our work, let's solve the first equation using #-3# and #-4# as #x#and #y#
#4x-3y=0#

If our answers are correct, we should find our solution to be #0#!
#4(-3)-3(-4)#
#-7--7#
#-7+7#
#0=0#
We were right!