# Equations with no solutionsExplain why the equations haven't solutions ? x+24=10 x natural number x+y+24=10 y,x natural.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

x+24=10

x+y+24=10

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.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.