document.write( "Question 1126889: Find values for h and k so that the system has infinitely many solutions. Write answers as integers or fractions in lowest terms. \r
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\n" ); document.write( "\n" ); document.write( "−8x − 6y = h
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Algebra.Com's Answer #743213 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
Since we have linear equations(lines), we want them to have the same slope and y intercept
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\n" ); document.write( "equation 1
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\n" ); document.write( "−8x − 6y = h
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\n" ); document.write( "-6y = 8x +h
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\n" ); document.write( "y = -8x/6 -h/6
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\n" ); document.write( "y = -4x/3 -h/6
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\n" ); document.write( "equation 2
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\n" ); document.write( "12x + ky = 24
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\n" ); document.write( "ky = -12x +24
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\n" ); document.write( "y = -12x/k +24/k
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\n" ); document.write( "the slopes must be equal, therefore
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\n" ); document.write( "-4/3 = -12/k
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\n" ); document.write( "cross multiply the fractions
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\n" ); document.write( "-4k = -36
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\n" ); document.write( "k = 9
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\n" ); document.write( "y intercepts must be equal
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\n" ); document.write( "-h/6 = 24/k
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\n" ); document.write( "we know k = 9
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\n" ); document.write( "-h/6 = 24/9 = 8/3
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\n" ); document.write( "-3h = 48
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\n" ); document.write( "h = -16
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\n" ); document.write( "h = -16 and k = 9
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\n" ); document.write( "check the answer
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\n" ); document.write( "equation 1
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\n" ); document.write( "-8x -6y = -16
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\n" ); document.write( "-4x -3y = -8
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\n" ); document.write( "4x +3y = 8
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\n" ); document.write( "equation 2
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\n" ); document.write( "12x + 9y = 24
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\n" ); document.write( "4x +3y = 8
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