document.write( "Question 625456: I need to know how to set up problems like this the sum of two numbers is 25 one number is twice the second plus seven what are the two two number? \n" ); document.write( "

Algebra.Com's Answer #393557 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
You start by calling the numbers x and y.
\n" ); document.write( "For the statement \"the sum of two numbers is 25\" it does not matter what number is x and what number is y.
\n" ); document.write( "\"The sum of two numbers is 25\" can be written as $\"x%2By=25\"$
\n" ); document.write( "That is one equation.
\n" ); document.write( "When there is talk that sets the numbers apart, you have to decide which one is which.
\n" ); document.write( "Since the problem says that \"one number is twice the second plus seven\", you could say that x is the \"one number\" and y is \"the second number\".
\n" ); document.write( "Then you write that x is twice y (2y) plus 7, as
\n" ); document.write( " $\"x=2y%2B7\"$ as your second equation.
\n" ); document.write( "The two equations form the system of linear equations:
\n" ); document.write( " $\"system%28x%2By=25%2Cx=2y%2B7%29\"$
\n" ); document.write( "That system begs to be solved by substitution.
\n" ); document.write( "You can just substitute the expression $\"2y%2B7\"$ for $\"x\"$
\n" ); document.write( "in the first equation to get
\n" ); document.write( " $\"2y%2B7%2By=25\"$ --> $\"3y%2B7=25\"$ --> $\"3y=18\"$ --> $\"highlight%28y=6%29\"$
\n" ); document.write( "Then, you just plug that value for $\"y\"$ into $\"x=2y%2B7\"$
\n" ); document.write( "to find $\"x=2%2A6%2B7\"$ --> $\"highlight%28x=19%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );