document.write( "Question 52000: Find the exact decimal value for k where the system of equations has no solution.\r
\n" ); document.write( "\n" ); document.write( "5x - 4y = 8, 10x + ky = 11\r
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Algebra.Com's Answer #38319 by rchill(405) $\"\"$ $\"About$

You can put this solution on YOUR website!
To have no solution, the lines must be parallel, which means they have the same slope. So first solve both equations for y and you get $\"y=expr%285%2F4%29x-2\"$ and $\"y=-expr%2810%2Fk%29x%2B11%2Fk\"$ . That means that the slope of the first equation is $\"5%2F4\"$ and for the second it's $\"-expr%2810%2Fk%29\"$ . Because they must be the same slope for parallel lines, k must have a value of -8. To verify that, graph both equations to see if they are indeed parallel.
\n" ); document.write( " $\"graph%28200%2C200%2C-5%2C5%2C-5%2C5%2C5x%2F4-2%2C10x%2F8-11%2F8%29\"$ \n" ); document.write( "

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