Question

The sum of two numbers is 80 and their difference is 22. Find the two numbers.

show steps and check stepi had tryed and failed

Answer 1

x+y=80
x-y=22

solve for x and y

Answer 2

gotthat part written out

Answer 3

using elimination method:

add the two equations ....to eliminate y

Answer 4

i dont know how i have so far
x+y=80
x-y=22
y=x+22
x+x+22

Answer 5

Alright using substitution method instead:\[\large x+y=80\]
\[\large x-y=22\]\[\large \implies y=x+22\]

now substitute \(x+22\) for \(y\) in the first equation:
\[\Large \implies x+(x+22)=80\]

Answer 6

sorry that should be \(\LARGE x-22\)

\[\large y=x-22\]

\[\Large \implies x+x-22=80\]

Answer 7

i am still lost

Answer 8

we figured that y=28 andx=52 butwe cant get the check step andhow we got it sincemy nephew can only fgureit in his head

Answer 9

\[x-y= 22\]\[\implies x-y+y=22+y\]\[\implies x=22+y\]\[\implies x-22=22+y-22\]\[\implies x-22=y\]

Answer 10

because \(y= x-22\), we can substitute x-22 instead of y in the first equation

\(x+y=80\) becomes \(\implies \large x+x-22=80\)

Answer 11

\[2x-22=80\]\[\implies \large2x=80+22=102\]\[\implies \Large x={102\over2}=\huge51\]

Answer 12

plug x=51 in any of the two original equations to get y=29

Answer 13

You can use the elimination method by adding the two equations:

\[\Large\ \ x+y=80\]\[\Large\ \ x-y=22\]\[\Large \overline{ 2x+0=102}\]

Answer 14

ty

Answer 15

the numbers are 51 and 29