Which of the following ordered pairs are solutions to the system of equations below?
2 answers:
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Answer:
46
Step-by-step explanation:
Let represent a number with
in the ten's position and
is the one's position.
This means actually has value of
.
We are given the sum of those digits of is 10; this means
.
It says if 18 is added to the number , then the result is
.
So has value
and
has value
.
We are given then:
Subtract on both sides:
Simplify:
Subtract on both sides:
Divide both sides by 9:
Rearrange by commutative property:
So the system of equations we want to solve is:
-------------------------Add equations together (this will eliminate the variable and allow you to go ahead and solve for
:
Divide both sides by 2:
Simplify:
If and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.