Solve the following system of equations x + y =-5 -3x - y =7

X+y= -5>【1】×3
-3x-y=7>【2】×1

3x+3y= -15
-3x-y=7

So,

2y=-8
y=-4

And

-3x-y=7
-3x-(-4)=7
-3x=7-4
x=-1

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1)   x + y = -5      (Add both the equations(equation1 + equation2))
2)  -3x - y = 7
     
       -2x     = 2
        x   = -1

x + y = -5 
-1 + y = -5 (put the value of x = -1)
y = -5 + 1
y = -4
 So, x = -1
and y = -4

 Alternate method:-
1)   x + y = -5
      x = -5 - y

2)   -3x - y = 7
      -3(-5 - y) - y = 7 (take the value of x = - 5 - y from equation(1) and put in                  15 + 3y - y = 7                                                                          equation(2))     
       2y = 7 - 15
        2y = -8
         y  =  -4
   
  1)    x = - 5 - y              (put the value of y = -4 in equation(1))
         x = - 5 -(-4)            (negative * negative = positive)      
         x = - 5 + 4               
          x = -1

    - x = -1
                    y = -4

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

the value of x is equal to 0.