text: # algebra
  
  posted by on .
  
  how do you use the substitution method to solve the linear system?
  -2x-5y=7
  7x=y=-8
  
  • algebra - ,
  
  Is the second line supposed to be 7x + y = -8, or 7x - y = -8? You sweem to have inserted a second equal sign by mistake.
  
  Whichever it is, use the second equation to derive an equation for y in terms of x. Then substitute that "y" value into the first equation, and it will be an equation in x only. Solve it.
  
  • algebra - ,
  
  7x+y=-8
  i don't understand what you mean. could you possibly do an example?
  
  • algebra - ,
  
  We have this:
  
  How do you use the substitution method to solve the linear system?
  
  -2x - 5y = 7...Equation A
  
  7x - y = -8...Equation B
  
  The idea is to isolate y OR x (your choice) and then plug that into EITHER Equation A or B (your choice).
  
  I will isolate y in Equation B.
  
  7x - y = -8...Equation B
  
  -y = -7x - 8
  
  y = (-7x - 8)/-1
  
  y = 7x + 8
  
  Do you see that we NOW know that y is 7x + 8?
  
  To find x, I will plug 7x + 8 into EITHER Equation A or B.
  
  I will choose Equation A.
  
  -2x-5y = 7...Equation A
  
  -2x - 5(2x + 8) = 7
  
  -2x - 10x - 40 = 7
  
  -12x - 40 = 7
  
  -12x = 7 + 40
  
  -12x = 47
  
  x = 47/-12
  
  x = -47/12...Value for x.
  
  We just found the value of x and it is
  -47/12. See it above?
  
  We now plug our value for x into EITHER Equation A or B to find the value of y.
  
  I will choose Equation A again.
  
  -2x -5y = 7...Equation A
  
  -2(-47/12) - 5y = 7
  
  47/6 - 5y = 7
  
  -5y = -47/6 + 7
  
  -5y = -5/6
  
  y = -5/6 divided by -5
  
  y = 1/6
  
  The solution for this system of linear equations in two variables is
  x = -47/12 and y = 1/6.
  
  We can also write the solution this way:
  
  (-47/12, 1/6) = (x, y), where x represents -47/12 and y represents 1/6.
  
  Done!
  
  • algebra - ,
  
  7x+y=-8
  
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