SOLUTION: 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

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(52795)   (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: .
RELATED QUESTIONS
Solve the system using the substitution method. If the system has no solution or an... (answered by Alan3354)
Solve the system using the substitution method. If the system has no solution or an... (answered by ilana)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by lefty4ever26)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by rapaljer)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by edjones)
-2x + 0y = -14 x + 11y = 18 Solve using the substitution method. Show your work. If... (answered by mananth)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by stanbon)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by rfer)
Solve using the substitution method. Show your work. If the system has no solution or an... (answered by jorel1380)