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#
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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#
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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" "#
Now add the 2 equations
#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#
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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)#.
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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#
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