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Question 87234: Please help me on how to do this problem:
Determine the constant k so that ( -2,3) will satisfy the equation - kx-4y= -k
PLEASE HELP ME!!!!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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-kx - 4y= -k
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This equation must be true for the point (-2, 3) which means it must be hold true when
x is -2 and y is +3.
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Substitute those values in for x and y to get:
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-k(-2) -4(+3) = -k
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Multiply out the two terms on the left to get:
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+2k - 12 = -k
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Next, we need to get the terms containing k on one side of the equation and everything
else on the other side. We can get rid of the -k on the right side by adding +k to both
sides. On the right side the addition of -k and +k results in zero. And on the left side
the +k adds to the +2k. This results in:
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3k - 12 = 0
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Next add 12 to both sides to get rid of the -12 on the left side. With this addition
the equation becomes:
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3k = 12
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Solve for k by dividing both sides by 3 ... the multiplier of k. The result of this
division give us the value of k as:
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k = 12/3 = 4
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check the answer by substituting 4 for k in the original given equation. When you do,
the equation:
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-kx - 4y= -k
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becomes:
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-4x -4y = -4
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Divide all terms by -4 to get:
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x + y = 1
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Does (-2, 3) satisfy this equation? Substitute -2 for x and +3 for y to get:
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-2 + 3 = 1
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Add the terms on the left side and you get:
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1 = 1
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This verifies that k = 4 because it works in the equation and (-2, 3) is a solution
when k has this value.
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Hope this helps you to understand the problem.
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