document.write( "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! \n" ); document.write( "
Algebra.Com's Answer #327834 by Theo(13342)\"\" \"About 
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both get the same result.
\n" ); document.write( "substitution takes one of the equations and solves it in terms of one of the unknowns in relationship to the other unknown.
\n" ); document.write( "elimination multiples one equation and then adds or subtracts that equation from the other equation in order to eliminate one of the unknowns.
\n" ); document.write( "the end result is the same.
\n" ); document.write( "here's a simple set of equations that will be solved both ways:
\n" ); document.write( "they are:
\n" ); document.write( "x + y = 15
\n" ); document.write( "x + 2y = 20
\n" ); document.write( "solve by substitution first.
\n" ); document.write( "solve for y in the first equation to get y = 15-x
\n" ); document.write( "substitute in the second equation to get x + 2*(15-x) = 20
\n" ); document.write( "remove parentheses to get x + 30 - 2x = 20
\n" ); document.write( "combine like terms to get -x + 30 = 20
\n" ); document.write( "subtract 30 from both sides of the equation to get -x = 20-30 which becomes -x = -10 which becomes x = 10
\n" ); document.write( "now that you know that x = 10, you can solve for y in either equation to get y = 5.
\n" ); document.write( "solve by elimination next.
\n" ); document.write( "multiply first equation by 2 to get:
\n" ); document.write( "2x + 2y = 30
\n" ); document.write( "x + 2y = 20
\n" ); document.write( "subtract second equation from first equation to get:
\n" ); document.write( "x = 10
\n" ); document.write( "now that you have solved for x, you can solve for y to get y = 5
\n" ); document.write( "both methods got you x = 10 and y = 5.
\n" ); document.write( "in this particular case, elimination method was easier.
\n" ); document.write( "it did not solve for y in terms of x or x in terms of y.
\n" ); document.write( "it just eliminated that variable from the equation to allow you to solve for the remaining unknown variable.\r
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