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Title: Can someone solve these linear equations using the substitution method? Post by: JUJUBEEM on Feb 18, 2013 8x-y=-15
3x+6y=-12 And 7x+7y=-7 3x+3y=-3 Can someone please solve these using EVERY step? Also, does anyone know of any FREE substitution method calculators that show the work? Please and thank you. Title: Can someone solve these linear equations using the substitution method? Post by: lelien on Feb 18, 2013 8x - y= -15 ===> y = 8x + 15
3x + 6y = -12 3x + 6(8x + 15) = -12 3x + 48x + 90 = -12 51x = -102 x = -2 ===== y = 8(-2) + 15 y = -16 + 15 y = -1 ===== Do the other one similarly. Title: Can someone solve these linear equations using the substitution method? Post by: nursestudent on Feb 18, 2013 (A)
Given: 8x - y = -15 ................(1) 3x + 6y = -12 ..............(2) From eqn. (1), we have: y = 8x + 15 ................(3) Substituting the value of y from eqn. (3) into eqn. (2), we have: 3x + 6(8x + 15) = -12 => 3x + 48x + 90 = -12 => 51x = -102 => x = -2 Substituting this value of x in eqn. (3), we have: y = 8*(-2) + 15 => y = -16 + 15 => y = -1 Answer: (x, y) = (-2, -1) (B) Given: 7x + 7y = -7 ...........(1) 3x + 3y = -3 ...........(2) Dividing both sides of eqn. (1) by 7, we have: x + y = -1 .............(3) Dividing both sides of eqn. (2) by 3, we have: x + y = -1 ..............(4) Equations (3) and (4) are the same equation. Hence, the given system of linear equations does not have a unique solution, i.e. there are infinitely many solutions. Answer: There are infinitely many solutions of the given system of linear equations. [ A few examples are: (x, y) = (2, -3) or (3, -4) or (4, -5) or (5, -6). You could go on an on like this; there are infinite solutions that satisfy both the given equations. ] About calculators: I have no idea about any such calculator. |