Question 545941: without graphing answer the following questions about the system, x-y=7,
9x=9y+4.
Does this system have a solution?
yes or no?
Is the system inconsistent, are the equations dependent, or neither?
What does this graph look like? Intersecting lines? One line? Or parallel lines?
Thank you for your help
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! you have two equations in your system:
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x - y = 7
9x = 9y + 4
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since these both describe straight lines, it is useful to convert them into standard slope-intercept form: y = mx + b:
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x - y = 7
y = x - 7
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9x = 9y + 4
y = x - 4/9
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in both, the slopes are m = 1; however, the y intercepts are different:
1st eqn: b = -7
2nd eqn: b = -4/9
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Is there a solution to this system? No, there is no common point which solves both equations. This is also the meaning of an inconsistent system of linear equations: there is no solution to the system.
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The graph would like two parallel lines with positive slope upwards to the right.
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cheers,
Lee
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