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What is the best method to solve this system? 2x + 8y = -6 and -2x - 4y = 36si need iii

The best is method of elimination of the variable (add the equations or subtract one equation from the other (whichever is appropriate) to form a new equation that only contains one variable.).
2x + 8y = -6    .......(1)
+
-2x - 4y = 36    .......(2)
↓     ↓      ↓
-----------------------
0 +  4y = 30  (We have added equals to equals, and addition eliminates x)
4y/4 = 30/4 -------------> y = 7.5

Substituting y = 7.5 in (1) gives:
2x + 8 · 7.5 = -6
2x + 60 = -6
- 60    -60
2x = -66
2x/2 = -66/2
x = -33                     The solution is (-33 , 7.5)
Check: 1. 2 · (-33) + 8 · 7.5 = -6             2. -2 · (-33) - 4 · 7.5 = 36
-66      +   60     = -6                     66       -   30     = 36
-6 = -6                                        36 = 36

Hi, Teresa.

I don't know if I would say one method is best over another, but I would say that I would prefer to use the Elimination Method on this system.  The Elimination Method is when you add the equations vertically, and one of the variable terms conveniently "cancel each other out."

2x   +   8y   = - 6
-2x    -   4y   =  36
4y    =   32

See how the two x-terms cancelled each other out?  This leaves us a much simpler single variable equation to solve.  Once you get your answer for y, be sure to substitute its value into one of the equations and solve for x.

Hope this helps.