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How do I do this problem using the substitution method. x - 9y = -66, -x - 5y = -46

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2 Answers

X -9Y = -66
-X -5Y = -46                   Solve one the the variables in terms of other, and substitute in the other equation.
                                      and becomes equation with one variable/
 
   X = 46 - 5Y   from 2nd equation.
   
      46 - 5 Y - 9Y = -66
 
       66 + 46  = 14 Y
 
       112 = 14 Y
 
        Y = 112/ 14 = 8                            
         
        Substitute back into 1st equation:
 
            X = 46 - 5(8) = 8
     
          X =  6 
Hi Quanda;
 
 
Let's take the first equation...
x - 9y = -66
Let's isolate x by adding 9y to both sides...
9y+x-9y=-66+9y
x=-66+9y
 
Let's substitute this into the other equation...
-x - 5y = -46
-(-66+9y)-5y=-46
A negative of a negative number results in positive, -(-66)=66 and
a negative of a positive number results in negative, -(9y)=-9y.
66-9y-5y=-46
66-14y=-46
Let's subtract 66 from both sides...
-66+66-14y=-46-66
-14y=-112
Let's divide both sides by -14...
(-14y)/-14=-112/-14
A negative number divided by a negative number results in a positive number.
y=8
 
Let's return to the original equations...
x - 9y = -66, -x - 5y = -46
x-9y=-66
Let's plug-in y=8...
x-[9(8)]=-66
x-72=-66
Let's add 72 to both sides...
72+x-72=-66+72
x=6
 
The second equation...
-x-5y=-46
Let's plug-in y=8 and x=6 to verify...
-6-[5(8)]=-46
-6-40=-46
-46=-46