document.write( "Question 1109954: solve the following equation by row reducing to echlon form
\n" ); document.write( "3x+5y=9
\n" ); document.write( "2x+3y=5 \n" ); document.write( "

Algebra.Com's Answer #725003 by greenestamps(13209) $\"\"$ $\"About$

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\n" ); document.write( "There are many different possible paths to take in reducing the matrix to row echelon form....

\n" ); document.write( "The original matrix A:
\n" ); document.write( " $\"matrix%282%2C3%2C3%2C5%2C9%2C2%2C3%2C5%29\"$

\n" ); document.write( "First step: make A(1,1)=1.
\n" ); document.write( "You could divide row 1 by 3; but that introduces fractions. It is already easy enough, in the Gauss-Jordan elimination process, to make simple arithmetic errors, without introducing fractions. So my choice for making A(1,1)=1 id to replace row 1 with (row 2 - row 1):
\n" ); document.write( " $\"matrix%282%2C3%2C1%2C2%2C4%2C2%2C3%2C5%29\"$

\n" ); document.write( "Step 2: make A(2,1)=0.
\n" ); document.write( "We have no choice here; we need to use the 1 in A(1,1) to make A(2,1) equal to 0. Replace row 2 with (row 2 - 2*row 1):
\n" ); document.write( " $\"matrix%282%2C3%2C1%2C2%2C4%2C0%2C-1%2C-3%29\"$

\n" ); document.write( "Step 3: make A(2,2)=1.
\n" ); document.write( "This one is simple -- multiply row 2 by -1:
\n" ); document.write( " $\"matrix%282%2C3%2C1%2C2%2C4%2C0%2C1%2C3%29\"$

\n" ); document.write( "Step 4: make A(1,2)=0.
\n" ); document.write( "Again we have no choice but to use the 1 in A(2,2). Replace row 1 with (row 1 - 2*row 2):
\n" ); document.write( " $\"matrix%282%2C3%2C1%2C0%2C-2%2C0%2C1%2C3%29\"$

\n" ); document.write( "The matrix is now in reduced row echelon form.

\n" ); document.write( "The solution to the system is x=-2, y=3. \n" ); document.write( "

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