Question

[DECIDE WHEATHER THE GIVEN ORDERED PAIR IS A SOLUTION OF THE EQATION] HOW DO U SOLVE PROBLEMS LIKE THESE Y=-2 (-2,-2)

Answer 1

Systems with no solution and infinite solutions When you are trying to calculate the solution of a system of linear equations, you can will arrive at one of three distinct cases:
These cases only apply to systems of two lines. If you are working with systems with three or more linear equations (lines), you cannot use the blanket generalizations made below.
The system has exactly 1 solution.
Systems have 1 and only 1 solution when the two lines have different slope. Think about it, if the two lines have different slopes then eventually at some point they must meet. After all the lines are not parallel.

system has no solutions
Systems have no solution when the lines are parallel (ie have the same slope) and the lines have different y-intercepts.
As an example look at the following two lines
Line 1: y = 5x +13 Line 2: y = 5x + 12

The system has infinite solutions
Systems have infinite solutions when the lines are parallel and the lines have the same y-intercept. If two lines have the same slope (ie are parallel) and the same y-intercept, they are actually the same exact line. In other words, systems have infinite solutions when the two lines are the same line!
As an example consider the following two lines
Line 1: y = x +3 Line 2: 2y = 2x +6
These two lines are exactly the same line. If you multiply line 1 by two you get line 2.


The solution of the system of equations on the left is (2,2) which marks the point where the two lines intersect.