document.write( "Question 972322: Find the value of k if 5x + 7y = k and 10x +19y = 3 have infinite number of solutions \n" ); document.write( "

Algebra.Com's Answer #594661 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the value of k if 5x + 7y = k and 10x +19y = 3 have infinite
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document.write( "This is impossible. Both the slopes and the y-intercepts must be the same in\r\n" );
document.write( "both equations in order for two equations to have an infinite number of\r\n" );
document.write( "solutions.   \r\n" );
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document.write( "No matter what value k takes on, the slope of 5x + 7y = k is the same. To show\r\n" );
document.write( "that they do not have the same slope, we put them both in slope-intercept\r\n" );
document.write( "form:  \"y = mx + b\":\r\n" );
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document.write( "5x + 7y = k\r\n" );
document.write( "     7y = -5x + k\r\n" );
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document.write( "Comparing with y = mx + b the slope is  and the y-intercept is\r\n" );
document.write( "the point \r\n" );
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document.write( "For the other equation:\r\n" );
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document.write( "10x + 19y = 3\r\n" );
document.write( "      19y = -10x + 3\r\n" );
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document.write( "Comparing with y = mx + b the slope is  and the y-intercept is\r\n" );
document.write( "the point \r\n" );
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document.write( "They do not have the same slope, so no matter what value of k we use,\r\n" );
document.write( "there will always be exactly one solution.\r\n" );
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document.write( "Edwin

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