True or false ? 5 is a solution of 19=14-y

Asked on by chealon1

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thanatassa's profile pic

thanatassa | College Teacher | (Level 1) Distinguished Educator

Posted on

In order to determine whether the statement "5 is a solution of 19=14-y" is true or false you need to solve the equation. Since the only variable, or unknown, in the equation is "y" this means that you need to solve the equation for "y", i.e. find out the value of "y".  To find the value of "y" you should try to isolate "y" so that it is the only thing on one side of the equation. To do this, add y to both sides of the equation:

19 + y = 14 (-y + y)

Since +y and -y cancel out, this leaves:

19+y =14

Now subtract 19 from both sides of the equation to isolate y:

(19-19) +y =  14-19


0+y = -5

which means

y = -5

And thus the answer +5 was false.

schwangmath's profile pic

schwangmath | High School Teacher | (Level 1) Adjunct Educator

Posted on

"Solutions" must make the equation a true statement.  Verify this by substituting your proposed solution into the given equation.

1.   19 = 14 - y            original equation

       19 = 14 - 5           substitution of proposed value

       19 = 9                 True or False?   -    FALSE!

2.  Determine whether your simplified statement is true or false.  Since 19 does not equal 9, this statement is false.  If the resulting statement is false, the proposed value is not a solution.


Therefore, 5 is not a solution of 19 = 14 - y.

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