document.write( "Question 939043: One half of a larger number, plus three times another number is equal to 9. Two thirds a larger number minus twice a smaller number is 6. \n" ); document.write( "

Algebra.Com's Answer #572106 by srinivas.g(540) $\"\"$ $\"About$

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let x, y be the larger & smaller number respectively\r
\n" ); document.write( "\n" ); document.write( "One half of a larger number, plus three times another number is equal to 9
\n" ); document.write( " $\"+%28x%2F2%29%2B+3%2Ay++=+9+\"$ ...............eq(1)
\n" ); document.write( " Two thirds a larger number minus twice a smaller number is 6.
\n" ); document.write( " $\"%282%2F3%29+%2Ax+-+2y++=6\"$ ...............eq(2)
\n" ); document.write( " we need to solve above equations to get the answers
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Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
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We'll use substitution. After moving 3*y to the right, we get:
\n" ); document.write( " $\"0.5%2Ax+=+9+-+3%2Ay\"$ , or $\"x+=+9%2F0.5+-+3%2Ay%2F0.5\"$ . Substitute that
\n" ); document.write( " into another equation:
\n" ); document.write( " $\"0.666666666666667%2A%289%2F0.5+-+3%2Ay%2F0.5%29+%2B+-2%5Cy+=+6\"$ and simplify: So, we know that y=1. Since $\"x+=+9%2F0.5+-+3%2Ay%2F0.5\"$ , x=12.
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\n" ); document.write( " Answer: $\"system%28+x=12%2C+y=1+%29\"$ .
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\n" ); document.write( "\n" ); document.write( "result: larger number = 12
\n" ); document.write( " smaller number = 1 \n" ); document.write( "

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