Explanation:
Q1: The solution of a system of two linear equations in two variables is the point where their graphs intersect. At that point, the (x, y) pair satisfies both equations.
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Q2: There will be no solution when the lines representing the equations do not intersect. That will only happen when they are parallel. (We say the equations are "inconsistent.")
There will be infinitely many solutions when the lines overlap. That is, the equations for them are essentially the same equation. (We say the equations are "dependent.")
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Q3: Elimination is easiest when the coefficients of one of the variables are opposites of each other, or if one is a factor of the other. Substitution is easiest if one of the equations is easily put in the form x = ( ) or y = ( ).
If neither or both conditions hold, the choice is by student preference. (In this latter case, solution using Cramer's rule may be simplest.)
