Adding the 2 equations, ax by ax on both sides, will eliminate y leaving an equation in x that we deserve to solve.

You are watching: The sum of two numbers is 12 and the difference is 8

#rArr(1)+(2)" gives"#

#(x+x)+(color(red)(-y+y))=(4+12)#

#rArr2x=16#

divide both sides by 2

#(cancel(2) x)/cancel(2)=16/2#

#rArrx=8#

Substitute this value right into equation ( 1 ) and solve because that y

#rArr8+y=12#

#rArry=12-8=4#

#"Thus the 2 numbers room " 8" and " 4#

LM
Mar 19, 2017

#a=4##b=8#

Explanation:

let these two numbers be #a# and also #b#.

#a+b=12##a-b=4#

if you add the 2 equations:

#a+b=12##a-b=4#

#2a+0 = 8##2a = 8#

divide through #2#:#a = 4#

substitute:#a+b = 12##4+b=12##b=12-4##=8#

#a=4##b=8#

#8+4=12##8-4=4#

David Drayer · EZ as pi
Mar 19, 2017

There room two number so you require two equations. Settle for one variable ( number) and also then substitute and also solve for the other.

#x = 8 and also y = 4#

Explanation:

Let #x# same one number and also #y# the various other number.

One equation would certainly be the sum of the numbers.

#x + y = 12#

the other equation would certainly be the difference of the 2 numbers

#x-y = 4" "#

#x +y = 12 " " and also " "x -y = 4" "#(adding #+ y and also -y = 0#)

so #2x = 16" "# currently divide both political parties by 2

# (2x)/2 = 16/2" "# This offers

#x = 8# now substitute x right into one the the equations and also solve for y

#8 + y =12" "# subtract 8 native both sides

# 8 -8 +y = 12 -8 " "# This offers

#y = 4" "# put values right into the 2nd equation to check

#8 -4 = 4 #

#4 = 4" "# inspect

#x = 8 and also y = 4#

EZ as pi
Mar 22, 2017

The numbers room #4 and also 8#

Explanation:

Questions i beg your pardon involve 2 or much more numbers can be done utilizing one variable to define them all.

Let the smaller sized number it is in #color(red)(x)#.

See more: Pol I Am Doing Well, Thank You, I Am Doing Well — Thank You For Asking!

The difference in between the numbers is #4#.

The other number is #color(blue)(x+4)#

Their amount is #12#

#color(red)(x) +color(blue)(x+4) =12#

#2x = 12-4#

#2x = 8#

#x =4#

#:. X+4 = 8#

The numbers are #4 and also 8#