Question 948496: When graphing a system of linear inequalities how do you determine what the solution of the system is?
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! When we talk about the  of the system of equations, we mean the  of the variables that make both equations  at the  time.
There may be  pairs of  and  that make the  equation , and pairs of and that make the  equation , but we are looking for an and that would work in  equations.
A system of two linear equations in two unknowns might look like:
see their graph:
If equations are linear, their graphs will be straight lines that intersect at  particular   the system  a solution. Clearly this point is on  lines, and therefore its coordinates (, ) will satisfy the equation of either line. Thus the pair (, ) is the  and  solution to the system of equations.
Sometimes two equations might look different but actually describe the same line. For example, in
The second equation is just two times the first equation, so they are actually  and would both be equations of the line. Because the two equations describe the same line, they have all their points in common; hence there are an  number of solutions to the system.
see their graph:
If two lines happen to have the slope, but are  identically the line, then they will  intersect. There is  pair (, ) that could   equations, because there is no point (, ) that is simultaneously on both lines. Thus these equations are said to be  , and there is solution. The fact that they both have the  may not be obvious from the equations, because they are not written in one of the standard forms for straight lines. The slope is not readily evident in the form we use for writing systems of equations. (If you think about it you will see that the  is the negative of the coefficient of divided by the coefficient of ).
example:
see their graph:
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