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Question 1043938: Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.
x+y=7
6x+6y=42
Found 3 solutions by Timnewman, ikleyn, MathTherapy:
Answer by Timnewman(323)   (Show Source):
You can put this solution on YOUR website! Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.
x+y=7
6x+6y=42
solution
x+y=7----(1)
6x+6y=42--(2)
divide equ 2 by 6
x+y=7---(3)
equate equ 1 and 3
x+y=x+y
x-y+x-y=0
0=0
from the above,the system has no solution.
TIMNEWMAN
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.
x+y=7
6x+6y=42
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Divide the second equation by 6 (both sides),
and you will see that this equation become
x + y = 7,
exactly as the first equation is.
So, you have here the system of two equivalent (depending) equations.
The system has infinitely many solutions.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this.
x+y=7
6x+6y=42
x + y = 7 ----- eq (i)
6x + 6y = 42 ------ eq (ii)
Multiply eq (i) by 6 to get the exact equation as eq (ii)
Divide eq (ii) by 6 to get the exact equation as eq (i)
This means the equations are the SAME, and therefore there is an  .
However, you have to determine the answer using the SUBSTITUTION method. we then get:
x + y = 7____x = 7 - y ------ eq (i)
6x + 6y = 42 ------- eq (ii)
6(7 - y) + 6y = 42 -------- Substituting 7 - y for x in eq (ii)
42 - 6y + 6y = 42
- 6y + 6y = 42 - 42
0 = 0 ----- This is a TRUE statement and so, there is an: .
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