Answer:
the value of m for which the pair of simultaneous equations has indefinitely many solutions is m = 1.
Step-by-step explanation:
To find the value of m for which the pair of simultaneous equations 3x + my = 5 and (m + 2)x + 5y = m has indefinitely many solutions, we need to determine the condition that allows for infinitely many solutions.
The pair of simultaneous equations can be written as:
3x + my = 5 (Equation 1)
(m + 2)x + 5y = m (Equation 2)
To have infinitely many solutions, the two equations must represent the same line. This occurs when the coefficients of x and y in the two equations are proportional.
Let's equate the coefficients of x and y from the two equations:
From Equation 1: coefficient of x = 3
From Equation 2: coefficient of x = m + 2
Therefore, we have the equation: 3 = m + 2
Solving this equation for m, we subtract 2 from both sides:
m + 2 - 2 = 3 - 2
m = 1
So, the value of m for which the pair of simultaneous equations has indefinitely many solutions is m = 1.
