SOLUTION: Use Substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. 1/2x+2y=12 an

Algebra ->  Equations -> SOLUTION: Use Substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. 1/2x+2y=12 an      Log On


   

Question 181720: Use Substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. 1/2x+2y=12 and x-2y=6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1/2x + 2y = 12 and x - 2y = 6
:
Get rid of that annoying denominator, multiply the 1st equation by two
x + 4y = 24
Arrange for substitution:
x = (24 - 4y)
:
Substitute this for x in the 2nd equation
x - 2y = 6
(24-4y) - 2y = 6
-4y - 2y = 6 - 24
-6y = -18
6y = 18; multiplied both sides by -1
y = 18%2F6
y = 3
:
Find x using x = 24-4y
x = 24 - 4(3)
x = 24 - 12
x = 12
:
:
Check solution in the the 1st equation:
1/2x + 2y = 12
1%2F2*12 + 2(3) =
6 + 6 = 12