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gander123
- Senior | Next Rank: 100 Posts
- Posts: 50
- Joined: Tue Sep 25, 2012 12:47 am
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Hey folks
here comes the question:
"In the xy-plane, does the line with equation y=3*X +2 contain the point (r,s) ?
(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0
The correct answer here is:[spoiler] C (both together)[/spoiler]"
My thoughts:
When I first saw this question, my first intuition was to solve it algebraically. However, this turned out to be a complete disaster and would have killed my timing. So I think there must be another short way to do it.
Well, in order to proof whether a point (r,s) is on the linear equation in slope-intercept form, I think you need the coordinates. So the values for s = ? and r = ? need to be determined. However, taking either (1) or (2) would only provide us with s in terms of r or r in terms of s. Thus taking the two independent linear equations together, one could solve for exact values for r and s and thus these values could be substituted for x and y in the equation.
Is my assumption right ?! This would not need any calculations or algebra...
Cheers,
Tobi
here comes the question:
"In the xy-plane, does the line with equation y=3*X +2 contain the point (r,s) ?
(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0
The correct answer here is:[spoiler] C (both together)[/spoiler]"
My thoughts:
When I first saw this question, my first intuition was to solve it algebraically. However, this turned out to be a complete disaster and would have killed my timing. So I think there must be another short way to do it.
Well, in order to proof whether a point (r,s) is on the linear equation in slope-intercept form, I think you need the coordinates. So the values for s = ? and r = ? need to be determined. However, taking either (1) or (2) would only provide us with s in terms of r or r in terms of s. Thus taking the two independent linear equations together, one could solve for exact values for r and s and thus these values could be substituted for x and y in the equation.
Is my assumption right ?! This would not need any calculations or algebra...
Cheers,
Tobi
