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What are the values of m and n for which the system of linear equations has infinitely many solutions, 3x + 4y = 12, (m + n)x + 2(m - n)y = (5m - 1)?
- a)m = 1, n = 1
- b)m = 5, n = +1
- c)m = 1, n = 5
- d)m = 5, n = 2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
What are the values of m and n for which the system of linear equation...
For infinitely many solutions,
On solving these equations, we get
m = 5, n = +1
On solving these equations, we get
m = 5, n = +1
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Community Answer
What are the values of m and n for which the system of linear equation...
To determine the values of m and n for which the system of linear equations has infinitely many solutions, we need to solve the system of equations and analyze the conditions that lead to infinite solutions.
Given system of equations:
1) 3x + 4y = 12
2) (m - n)x + 2(m - n)y = (5m - 1)
Step 1: Simplify the equations
Equation 2 can be rewritten as:
(m - n)(x + 2y) = 5m - 1
Step 2: Check for parallel lines
For the system to have infinitely many solutions, the two equations must represent parallel lines. This means that their slopes should be equal. Since the given equations are in standard form, we can find the slopes by dividing the coefficients of x by the coefficients of y.
The slope of equation 1: m1 = -3/4
The slope of equation 2: m2 = (m - n)/2(m - n) = 1/2
Step 3: Set the slopes equal to each other
To find the values of m and n, we equate the slopes:
-3/4 = 1/2
Step 4: Solve for m and n
Cross multiply to solve for m and n:
-3 * 2 = 4 * 1
-6 = 4
Since -6 is not equal to 4, there is no solution for m and n that would make the slopes equal.
Step 5: Analyze the answer choices
Based on the analysis above, we can conclude that there are no values of m and n that would result in infinitely many solutions for the given system of equations. Therefore, none of the answer choices (A, B, C, D) are correct.
In conclusion, the correct answer is none of the above options.
Given system of equations:
1) 3x + 4y = 12
2) (m - n)x + 2(m - n)y = (5m - 1)
Step 1: Simplify the equations
Equation 2 can be rewritten as:
(m - n)(x + 2y) = 5m - 1
Step 2: Check for parallel lines
For the system to have infinitely many solutions, the two equations must represent parallel lines. This means that their slopes should be equal. Since the given equations are in standard form, we can find the slopes by dividing the coefficients of x by the coefficients of y.
The slope of equation 1: m1 = -3/4
The slope of equation 2: m2 = (m - n)/2(m - n) = 1/2
Step 3: Set the slopes equal to each other
To find the values of m and n, we equate the slopes:
-3/4 = 1/2
Step 4: Solve for m and n
Cross multiply to solve for m and n:
-3 * 2 = 4 * 1
-6 = 4
Since -6 is not equal to 4, there is no solution for m and n that would make the slopes equal.
Step 5: Analyze the answer choices
Based on the analysis above, we can conclude that there are no values of m and n that would result in infinitely many solutions for the given system of equations. Therefore, none of the answer choices (A, B, C, D) are correct.
In conclusion, the correct answer is none of the above options.
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What are the values of m and n for which the system of linear equations has infinitely many solutions, 3x + 4y = 12, (m + n)x + 2(m - n)y = (5m - 1)?a)m = 1, n = 1b)m = 5, n = +1c)m = 1, n = 5d)m = 5, n = 2Correct answer is option 'B'. Can you explain this answer?
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