Q: What are the possible solutions for a pair of linear equation?

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No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).

Yes.

No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.

All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.

In basic mathematics, a quadratic equation with a negative discriminant has no solutions. However, at a more advanced level you will learn that it has two solutions which form a complex conjugate pair.

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No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).

An ordered pair is a solution only of a linear equation in two variables - not any linear equation. Often the variables are denoted by x and y. If the first of the ordered pair is substituted for x in the equation, and the second for y, then the equation represents a true statement.

This is a linear algebra question and it is incomplete since there are no equation which have to be solved.

No, "pair" implies two and only two.

A solution of a linear equation is called a root or a solution. It is a value that satisfies the equation when substituted back into it.

One option is "cannot exist". The equation is linear and linear equations do not have vertices.

It is a linear equation in the two variables x and y. A single linear equation in two variables cannot be solved for a unique pair of values of x and y. The equation is that of a straight line and any point on the line satisfies the equation.

Yes.

No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.

There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)

If x = y, then the equation is true for any integer pair. Otherwise, the equation is not equivalent and is impossible.

All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.