document.write( "Question 954565: Six times ashleys age plus two times sydney's age equals 38. sydney's age is also three more than five times ashley's age/ how old is sydney? \n" ); document.write( "

Algebra.Com's Answer #583013 by aYummyNoodle(10) $\"\"$ $\"About$

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let x = Ashley's age.
\n" ); document.write( "let y = Sydney's age.
\n" ); document.write( "We can put the words into equations.
\n" ); document.write( " $\"6x%2B2y=38\"$ and
\n" ); document.write( " $\"y=5x%2B3\"$ .
\n" ); document.write( "There are many different ways of solving systems of linear equations which are graphing, substitution, and elimination. For this system I will use substitution and elimination.
\n" ); document.write( "SUBSTITUTION:
\n" ); document.write( "In the second equation, y is already isolated so we can just plug it in to the first equation:
\n" ); document.write( " $\"6x%2B2%285x%2B3%29=38\"$
\n" ); document.write( " $\"6x%2B10x%2B6=38\"$
\n" ); document.write( " $\"16x%2B6=38\"$
\n" ); document.write( " $\"16x=32\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "Now that we know that $\"x\"$ is 2, we can plug it in to the second equation:
\n" ); document.write( " $\"y=5%282%29%2B3\"$
\n" ); document.write( " $\"y=10%2B3\"$
\n" ); document.write( " $\"y=13\"$ .
\n" ); document.write( "After finding out that $\"x\"$ is 2 and $\"y\"$ is 13, we can write it in an ordered pair or a complete sentence.
\n" ); document.write( "(2,13) or:
\n" ); document.write( "Ashley is 2 years old and Sydney is 13 years old.
\n" ); document.write( "ELIMINATION:
\n" ); document.write( "In elimination, we need to line the variables and coefficients up, so
\n" ); document.write( " $\"6x%2B2y=38\"$ and
\n" ); document.write( " $\"-5x%2By=3\"$ .
\n" ); document.write( "Multiply the second equation by 2 to get:
\n" ); document.write( " $\"-10x%2B2y=6\"$ .
\n" ); document.write( "By subtracting one equation from another, we can eliminate the y's and get:
\n" ); document.write( " $\"16x=32\"$
\n" ); document.write( " $\"x=2\"$ .
\n" ); document.write( "So Ashley is 2 years old.
\n" ); document.write( "Plugging x back into the second equation, we get:
\n" ); document.write( " $\"-5%282%29%2By=3\"$
\n" ); document.write( " $\"-10%2By=3\"$
\n" ); document.write( " $\"y=13\"$ .
\n" ); document.write( "So Sydney is 13 years old.
\n" ); document.write( "Once again, Ashley is 2 years old and Sydney is 13 years old. \n" ); document.write( "

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