SOLUTION: What is the value of k if the line 2x - 3y = 5 is parallel to the line 2x + (k - 3)y = 7?

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Question 254322: What is the value of k if the line 2x - 3y = 5 is parallel to the line 2x + (k - 3)y = 7?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1 - solve this equation for y.
2x+-+3y+=+5
-3y+=+-2x+%2B+5
y+=+%282%2F3%29x+-5%2F3
Notice the slope is 2/3.
We want parallel slope so we use the same fraction 2/3.
Step 2 - solve this equation for y.
2x+%2B+%28k+-+3%29y++=++7
%28k+-+3%29y+=+-2x+%2B+7
y+=%28+-2%2F%28k-3%29%29x+%2B7%2F%28+k-3%29
The slope here is
-2/(k-3) which is equal to 2/3 as
-2%2F%28k-3%29+=+2%2F3
-6+=+2%28K-3%29
-6+=+2k+-+6
+k+=+0