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Let us solve the system and determine if we have a solution in the set of natural number.
We will use the elimination method.
We will subtract (1) from (2).
==> y = 0
Now to determine x we will substitute into (2).
==> x + y + 24 = 10
==> x + 0 + 24 = 10
==> x = -14
But we notice that x is NOT a natural number.
Natural numbers are positive integres and x is negative.
Then, there are no solutions to the system in the set of natural number.
Let's solve the equations to see why. We'll begin with the first equation:
x + 24 = 10
We'll isolate the variable to the left side. For this reason, we'll subtract 10 both sides:
x = 10 - 24
x = -14
Since the value of x has to be a natural number and -14 is not a natural number, the equation has no solution.
We'll solve the second equation:
x + y + 24 = 10
x + y = 10 - 24
x + y = -14
Since x and y are natural, so they are positive integer numbers, their sum could never be a negative integer number. Accordingly, there are no values for x and y to make the equality to hold.
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