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The system of equations above has how many solutions? (A) None (B) Exactly one (C) Exactly two (D) Exactly three (E) Infinitely many

Sol:

\(x-y=3\) is same as \(2x=2y+6\)

\(2x=2y+6\) Dividing both sides by 2; \(x=y+3\) Subtracting y from both sides; \(x-y=3\)

Thus, we have only one equation: \(x-y=3\) This has infinitely many solutions such as: x=3,y=0 x=100,y=97 x=-100,y=-103 x=0.001, y=-2.999 x=1, y=-2
_________________

The system of equations above has how many solutions?

(A) None (B) Exactly one (C) Exactly two (D) Exactly three (E) Infinitely many

I thought it's A as well. But OA is E?

I see your point ... A + B can be an infinite number of things... I suppose we answered it on the basis that the two solutions given gave us no CERTAIN solutions...

I think the question is a touch ambiguous, but I suppose we could have read it more closely.

The system of equations above has how many solutions?

(A) None (B) Exactly one (C) Exactly two (D) Exactly three (E) Infinitely many

I thought it's A as well. But OA is E?

I see your point ... A + B can be an infinite number of things... I suppose we answered it on the basis that the two solutions given gave us no CERTAIN solutions...

I think the question is a touch ambiguous, but I suppose we could have read it more closely.

seems ok but we cannot solve the equations do not provide any value for x and y.

Any single linear equation with more than 1 variable in it has infinite solutions (provided no constraints are given).

Edit: I do not see any ambiguity in the question.

The number of solutions for a linear equation is the number of possible values the variables can have so as to satisfy the equation. There are infinite possible values for the variables x & y in the given equation and therefore there are infinite solutions.