Solve the system of equations: 6(x+y)-12y = 0, 7(y+4)-(5y+3)=0.

Solution:

• The given system of equations is:
  • 1) \( 6(x+y) - 12y = 0 \)
  • 2) \( 7(y+4) - (5y+3) = 0 \)
• Simplify equation (2):
  • \( 7y + 28 - 5y - 3 = 0 \)
  • \( 2y + 25 = 0 \)
  • \( 2y = -25 \)
  • \( y = -\frac{25}{2} \)
• Substitute the value of y into equation (1):
  • First, simplify equation (1):
  • \( 6x + 6y - 12y = 0 \)
  • \( 6x - 6y = 0 \)
  • \( 6x = 6y \)
  • \( x = y \)
• Since \( x = y \) and \( y = -\frac{25}{2} \), then \( x = -\frac{25}{2} \).

Final Answer: The solution to the system of equations is \( x = -\frac{25}{2}, y = -\frac{25}{2} \).