Had this question on my test, got it wrong because I misunderstood it...
"Given the following dependent system of equations Ax + By = C and Dx + Ey = F
Where A,B,C,D,E, and F are non-zero Real Numbers, which of the following choice(s) would be an accurate representation of the solution set? For each choice explain why it does or why it does not represent the correct solution set.
a) { (x,y) | Ax + By = C}
b) (a,b)
c) {} , Empty Set
d) { (x,y) | Dx + Ey = F}
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"Given the following dependent system of equations Ax + By = C and Dx + Ey = F
Where A,B,C,D,E, and F are non-zero Real Numbers, which of the following choice(s) would be an accurate representation of the solution set? For each choice explain why it does or why it does not represent the correct solution set.
a) { (x,y) | Ax + By = C}
b) (a,b)
c) {} , Empty Set
d) { (x,y) | Dx + Ey = F}
Thanks for helping, add your question link and i'll answer yours! Thanks :)
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For (b), do you mean (a,d)? I think maybe this was a typo.
The answer is definitely a and d: since the system is dependent, one equation is just a multiple of the other, so they are describing the same line exactly. Because of this, the solutions are all the points (x,y) that satisfy either one of the equations (since they really are the same equation, just written differently, like how 4/5 and 8/10 are the same fraction written differently).
The answer is not (c). It would only be (c) if the equations were inconsistent, which would mean that they represent parallel, distinct (different) lines. (Two parallel lines that are not the same line, which would mean that they never meet, so there is no solution.)
The answer is definitely a and d: since the system is dependent, one equation is just a multiple of the other, so they are describing the same line exactly. Because of this, the solutions are all the points (x,y) that satisfy either one of the equations (since they really are the same equation, just written differently, like how 4/5 and 8/10 are the same fraction written differently).
The answer is not (c). It would only be (c) if the equations were inconsistent, which would mean that they represent parallel, distinct (different) lines. (Two parallel lines that are not the same line, which would mean that they never meet, so there is no solution.)