SOLUTION: Find the exact decimal value for k where the system of equations has no solution. 5x - 4y = 8, 10x + ky = 11 Help please! Thanks!

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Question 52000: Find the exact decimal value for k where the system of equations has no solution.
5x - 4y = 8, 10x + ky = 11
Help please! Thanks!
Answer by rchill(405) About Me  (Show Source):
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.
graph%28200%2C200%2C-5%2C5%2C-5%2C5%2C5x%2F4-2%2C10x%2F8-11%2F8%29