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When there is no ordered n-tuple (pair, triplet, quartet - depending on the number of dimensions) that satisfies both equations at the same time. In graph form, it is when the straight lines representing the two equations are non-intersecting.
In 2 dimensions non-intersection implies that the lines are parallel.
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What are the possible solutions for a pair of linear equation?
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
What is a system of equation that has no solution?
It is an inconsistent system of equations. --- Or perhaps you want examples? One pair of inconsistent equations: x + y = 4 x + y = 1 Another pair: y = x2 + 3 y = 1 (In the first equation of this pair, y is minimised when x = 0, when its value is 3. But the second equation claims that y = 1.)
Can a pair of linear equation have exactly two solutions?
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).
Can a pair of linear angles form a linear pair?
Yes.
Are supplementary angles necessarily a linear pair?
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
