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If 3x+4y=12 and (m+n)x+2(m-n)y=5m-1; then the values of m and n for which the above system has infinitely many solution is 
  • a)
    m = 5, n = -1 
  • b)
    m = 1, n = 5 
  • c)
    m = 5, n = 1 
  • d)
    None of the above 
Correct answer is option 'C'. Can you explain this answer?
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If3x+4y=12 and (m+n)x+2(m-n)y=5m-1;then the values of m and n for whic...
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If3x+4y=12 and (m+n)x+2(m-n)y=5m-1;then the values of m and n for whic...
Given equations:
1) 3x + 4y = 12
2) (m - n)x + 2(m - n)y = 5m - 1

To find the values of m and n for which the system has infinitely many solutions, we need to determine when the two equations are dependent or consistent.

Step 1: Rewrite equation 2 in terms of x and y:
(m - n)x + 2(m - n)y = 5m - 1
Simplifying, we get:
mx - nx + 2my - 2ny = 5m - 1
(mx - nx) + 2(my - ny) = 5m - 1
(m - n)x + 2(m - n)y = 5m - 1

Step 2: Compare the coefficients of x and y in equations 1 and 2:
Equating the coefficients, we have:
m - n = 3 ...(3)
2(m - n) = 4 ...(4)
From equation (4), we can simplify to:
m - n = 2 ...(5)

Step 3: Solve equations (3) and (5) simultaneously:
From equations (3) and (5), we have the system of equations:
m - n = 3
m - n = 2

Subtracting equation (5) from equation (3), we get:
0 = 1

Step 4: Analyzing the result:
The equation 0 = 1 is not possible. It implies that the system of equations is inconsistent, meaning there are no values of m and n that will make the system have infinitely many solutions.

Therefore, the correct answer is option 'd) None of the above'.
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If3x+4y=12 and (m+n)x+2(m-n)y=5m-1;then the values of m and n for which the above system has infinitely many solution isa)m = 5, n = -1b)m = 1, n = 5c)m = 5, n = 1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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