In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0
x=r and y=s, then question rephrased looks such as - 'does s=3r+2?'dreamv wrote:In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0
st(1) either 3r+2-s=0 or 4r+9-s=0. Both lead to s=3r+2 or s=4r+9. So, if s=4r+9, the first condition, i.e. s=3r+2 is not effected. Not Sufficient
st(2) the same logic here, either s=4r+6 or s=3r+2 Not Sufficient
Combining st(1&2): Since 4r+9 is not equal to 4r+6, or 9=!6 we conclude s=3r+2 is the only option possible, Sufficient
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