SOLUTION: 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?

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?
Answer by aYummyNoodle(10) (Show Source): You can put this solution on YOUR website!
let x = Ashley's age.
let y = Sydney's age.
We can put the words into equations.
and
.
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.
SUBSTITUTION:
In the second equation, y is already isolated so we can just plug it in to the first equation:

Now that we know that is 2, we can plug it in to the second equation:

.
After finding out that is 2 and is 13, we can write it in an ordered pair or a complete sentence.
(2,13) or:
Ashley is 2 years old and Sydney is 13 years old.
ELIMINATION:
In elimination, we need to line the variables and coefficients up, so
and
.
Multiply the second equation by 2 to get:
.
By subtracting one equation from another, we can eliminate the y's and get:

.
So Ashley is 2 years old.
Plugging x back into the second equation, we get:

.
So Sydney is 13 years old.
Once again, Ashley is 2 years old and Sydney is 13 years old.
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