SOLUTION: HELP!!!!! Im confused is there a difference between elimination and substitution in systems of equations i understand when to use them but i dont understand the difference thank yo

Question 478439: HELP!!!!! Im confused is there a difference between elimination and substitution in systems of equations i understand when to use them but i dont understand the difference thank you for the help!! great review for who ever answers have a beautiful day!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
both get the same result.
substitution takes one of the equations and solves it in terms of one of the unknowns in relationship to the other unknown.
elimination multiples one equation and then adds or subtracts that equation from the other equation in order to eliminate one of the unknowns.
the end result is the same.
here's a simple set of equations that will be solved both ways:
they are:
x + y = 15
x + 2y = 20
solve by substitution first.
solve for y in the first equation to get y = 15-x
substitute in the second equation to get x + 2*(15-x) = 20
remove parentheses to get x + 30 - 2x = 20
combine like terms to get -x + 30 = 20
subtract 30 from both sides of the equation to get -x = 20-30 which becomes -x = -10 which becomes x = 10
now that you know that x = 10, you can solve for y in either equation to get y = 5.
solve by elimination next.
multiply first equation by 2 to get:
2x + 2y = 30
x + 2y = 20
subtract second equation from first equation to get:
x = 10
now that you have solved for x, you can solve for y to get y = 5
both methods got you x = 10 and y = 5.
in this particular case, elimination method was easier.
it did not solve for y in terms of x or x in terms of y.
it just eliminated that variable from the equation to allow you to solve for the remaining unknown variable.

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