document.write( "Question 190068: Find the value of x+y in the following\r
\n" ); document.write( "\n" ); document.write( "[3x-2] [x y] = [42 4]
\n" ); document.write( "..........[3 4]\r
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\n" ); document.write( "\n" ); document.write( "*I added the dots so the 3 and 4 could go under the x and y as one matrix \n" ); document.write( "
Algebra.Com's Answer #142717 by cutepiscean5(19)\"\" \"About 
You can put this solution on YOUR website!
Find the value of x+y in the following\r
\n" ); document.write( "\n" ); document.write( "[3x-2] [x y] = [42 4]
\n" ); document.write( "..........[3 4]\r
\n" ); document.write( "\n" ); document.write( "Solution:
\n" ); document.write( "_________\r
\n" ); document.write( "\n" ); document.write( "we have a 1x2 matrix multiplied with a 2x2 matrix, which results in a 1x2 matrix again.\r
\n" ); document.write( "\n" ); document.write( "So, we first take the Left and side of this equation and multiply both the matrices and get the answers in terms of x and y.\r
\n" ); document.write( "\n" ); document.write( "we have:\r
\n" ); document.write( "\n" ); document.write( "[3x -2] [x y]
\n" ); document.write( "...............[3 4] \r
\n" ); document.write( "\n" ); document.write( "=> \r
\n" ); document.write( "\n" ); document.write( "we have got two terms which have been determined by multiplication, we now simplify them...\r
\n" ); document.write( "\n" ); document.write( "first element of the row is \"+%28+3x%5E2+-+6+%29+\"
\n" ); document.write( "and, second element of the row is \"+%28+3xy+-+8+%29+\"\r
\n" ); document.write( "\n" ); document.write( "now we compare both sides of the original equation and we get:\r
\n" ); document.write( "\n" ); document.write( "\"+3x%5E2+-+6+=+42+\" ..........(1)
\n" ); document.write( "and
\n" ); document.write( "\"+3xy+-+8+=+4+\" ............(2)\r
\n" ); document.write( "\n" ); document.write( "we have two equations and two variables x & y, we solve for them.\r
\n" ); document.write( "\n" ); document.write( "from equation (1) we have:\r
\n" ); document.write( "\n" ); document.write( "\"+3x%5E2+-+6+=+42+\"
\n" ); document.write( "=> \"+3x%5E2+=+42+%2B+6+\"
\n" ); document.write( "=> \"+3x%5E2+=+48+\"
\n" ); document.write( "=> \"+x%5E2+=+48%2F3+\"
\n" ); document.write( "=> \"+x%5E2+=+16+\"
\n" ); document.write( "=> \"+highlight%28x+=+4%29+\" or \"+highlight%28x+=+-4%29+\"\r
\n" ); document.write( "\n" ); document.write( "From equation (2),\r
\n" ); document.write( "\n" ); document.write( "when we plug in x = 4 , we get:\r
\n" ); document.write( "\n" ); document.write( "\"+3xy+-+8+=+4+\"
\n" ); document.write( "=> \"+3%284%29y+-+8+=+4+\"
\n" ); document.write( "=> \"+12y++=+4+%2B+8+\"
\n" ); document.write( "=> \"+12y+=+12+\"
\n" ); document.write( "=> \"+y+=+12%2F12+\"
\n" ); document.write( "=> \"+highlight%28y=1%29+\"\r
\n" ); document.write( "\n" ); document.write( "when we plug in x = -4 , we get:\r
\n" ); document.write( "\n" ); document.write( "\"+3xy+-+8+=+4+\"
\n" ); document.write( "=> \"+3%28-4%29y+-+8+=+4+\"
\n" ); document.write( "=> \"+-12y++=+4+%2B+8+\"
\n" ); document.write( "=> \"+-12y+=+12+\"
\n" ); document.write( "=> \"+y+=+12%2F%28-12%29+\"
\n" ); document.write( "=> \"+highlight%28y=-1%29+\"\r
\n" ); document.write( "\n" ); document.write( "Thus x+y = 4+1 = \"+highlight%285%29+\" or x+y = -4-1 = \"+highlight%28-5%29+\"\r
\n" ); document.write( "\n" ); document.write( "Hope this helps.\r
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