document.write( "Question 1060139: y=3x+2
\n" ); document.write( "3x+y=1
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Algebra.Com's Answer #675115 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Since you have 2 equations and 2 unknowns, the first thing is to try to solve for one of the variables. So long as the two equations are \"linearly independent\" (or not linearly-dependent) there will be a solution.
\n" ); document.write( "Linearly dependent means one equation can be re-arranged to exactly match the other (in essence, if they only \"look\" like two different equations but are in fact the same). Ok, enough on that…
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\n" ); document.write( "\"+y=3x%2B2+\" (1)
\n" ); document.write( "\"+3x%2By+=+1+\" (2)\r
\n" ); document.write( "\n" ); document.write( "(1) conveniently expresses y as a function of x, so let's substitute \"3x+2\" from (1) for \"y\" in (2):\r
\n" ); document.write( "\n" ); document.write( "\"+3x+%2B+%283x%2B2%29+=+1+\" (substituted \"3x+2\" for \"y\")
\n" ); document.write( "\"++6x+%2B+2+=+1+\"
\n" ); document.write( "\"+++6x+=+-1+\"
\n" ); document.write( "\"++x+=+-1%2F6+\"\r
\n" ); document.write( "\n" ); document.write( "If \"x=-1%2F6\" we can plug into (1) to get \"+y=3%28-1%2F6%29%2B2+=+-%281%2F2%29%2B%284%2F2%29+=+3%2F2+\"\r
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\n" ); document.write( "\n" ); document.write( "Ans: \"+x=-1%2F6+\" and \"+y=3%2F2+\"
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " (1) Does 3/2 = (3*(-1/6) + 2)?
\n" ); document.write( " 3/2 = (-3/6)+(12/6)
\n" ); document.write( " 3/2 = 9/6
\n" ); document.write( " 3/2 = 3/2 (ok)
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\n" ); document.write( " (2) Does 3(-1/6) + (3/2) = 1 ?
\n" ); document.write( " -(1/2) + (3/2) = 1 ?
\n" ); document.write( " 2/2 = 1 (ok)\r
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