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Solve using substitution: -y - 5x = -7 2y - 2x = 14

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2 Answers

First, solve one of the equations for one of the expressions:
 
-y -5x   =      -7
   +5x       +5x
 
-y = 5x - 7
 
y = -5x + 7
 
Then, substitue this for y in the other equation:
 
2(-5x + 7) -2x = 14
-10x +14 - 2x = 14
       -12x +14 = 14
               -14     -14
        -12x  =  0 
        -12        -12
           x    =  0
 
Then, solve the other equation by substituting this value for x.
y = -5x + 7
y = -5(0) +7
y = 0 + 7
y = 7
 
Now check your work:
-y-5x=-7  Solve where x=0 and y=7
-7 -5(0) = -7
-7-0=-7
-7 = -7
 
2y-2x=14 Solve where x=0 and y=7
2(7) -2(0) = 14
14-0=14
14=14
 
 
Sean
 
Lets label the two equations as A) and B):
 
A) -y-5x=-7
B) 2y-2x=14
 
First, we can solve equation A) for y, as follows:
 
Add 5x to both sides:  -y=-7+5X
Multiply both sides by -1:  y=7-5x
 
Next we can substitute this result for y into equation B), simplify, and solve for x as follows:
 
B) 2(7-5x)-2x=14
    14-10x-2x=14
    14-12x=14
        -12x=14-14
        -12x=0
             x=0  We have now solved for x.
 
Finally, we can plug 0 in for the value of x in either equation, to solve for y.  Let's use equation A):
 
A) -y-5x=-7
    -y-(5)(0)=-7
    -y=-7
     y=7  We have now solved for y.
 
We can check this result by substituting the values for x and y (0 and 7) back into each equation A) and B) to ensure that the values work.  This can be left to the student.
 
Hope this helps!
 
George T.