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2014-05-15T12:15:44+08:00

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Transform the equations into slope-intercep form:
Kx - 2y = 4      ––>      y = 
 \frac{K}{2} x -2
x + 3y = 7       ––>       y =  \frac{-1}{3} x +  \frac{7}{3}

For two equations to be parallel, their slope should be equal.
 \frac{k}{2}  \frac{-1}{3}
k =  -2/3
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2014-05-15T12:28:16+08:00

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Kx-2y=4   --equation 1
x+3y=7    --equation 2

Transform each equation to y=mx+b; where m=slope
y=(kx)/2 -2   equation 3
y=-x/3 +7     equation 4

Since parallel lines have the same slope, we equate:
(kx)/2 =-x/3    multiplying both sides by 1/x
k/2 =-1/3
k=-2/3

Substitute k=-2/3 in equation 3
y=-x/3 -2

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