Question

Find the value of m for which the pair of linear equation 2x+3y-7=0 and (m-1)x+(m+1)y=3(m+1) has many solution

Answer 1

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Answer 2

Let’s solve the problem.

From the first equation :

2x + 3y - 7 = 0

3y = 7 -2x

y = (7 - 2x) / 3

From the second equation :

(m - 1) x + (m + 1) y = 3m - 1

(m - 1)x = (3m - 1) - (m + 1)y

x = ((3m -1 ) - (m + 1)y) : (m - 1)

x = (3m - 1 -ym - y) : (m -1 )

Plugging x into the equation above,

y = ( 7 - 2x ) / 3 ………………. (1)

y = ( 7 - 2 ((3m - 1 - ym - y) : (m - 1))) / 3 …………….. (2)

y = ( 7 - ((6m - 2 - 2ym - 2y) : (m - 1))): 3 …………… (3)

y = (((7 (m - 1)) - (6m - 2 - 2ym - 2y)) : (m - 1)) : 3 …………….. (4)

y = ((7m - 7 -6m + 2 + 2ym + 2y) : (m -1 )) : 3 ……………… (5)

y = ((m - 5 + 2y (m + 1)) : (m -1 )) : 3 ……………… (6)

3y = (m - 5 + 2y (m + 1)) : (m - 1) ………………. (7)

3y (m - 1) = m - 5 + 2ym + 2y ……………. (8)

3ym - 3y = m -5 + 2ym + 2y ……………………. (9)

3ym - 2ym - 3y - 2y = m - 5 ……………………. (10)

ym - 5y = m - 5 ………………….. (11)

y (m- 5) = m - 5 ……………………….. (12)

y = 1. Which is the answer. ……………………. (13)

Or, following from (8)

y (3m - 3) = m - 5 + 2y (m + 1) …………………. (9)

y (3m - 3) - y (2m + 2) = (m - 5) ………………………… (10)

y (3m - 3 - 2m - 2) = (m - 5) ………………………….. (11)

y (m - 5 ) = (m - 5) ……………………… (12)

y = 1. Which is the answer. ………………………. (13)

We can see from the last equation (y = 1) that the equation has only one solution, which is y = 1, for whatever the value of m is.

So, the pair of linear equations 2x+3y-7=0 and (m-1)x+(m+1)y=3m-1 has only one solution which is y =1, for whatever the value of m is.

hope that my answer satisfies you. “,