Question

Find the values of m and n, such that the system of equations 2x + 3y = 7 and (m+n)x+(2m - n)y = 3(m +n + 1) has infinitely many solutions.
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Answer 1

Step-by-step explanation:

In case of infinitely many solutions,

a1/a2 = b1/b2 = c1/c2

2x + 3y = 7

a1 = 2, b1 = 3, c1 = 7

(m+n)x+(2m-n)y = 3(m+n+1)

a2 = m+n, b2 = 2m-n, c2 = 3(m+n+1)

2/m+n = 3/2m-n = 7/3(m+n+1)

By equating first two,

2/m+n = 3/2m-n

4m-2n = 3m+3n

m = 5n

By equating last two,

3/2m-n = 7/3(m+n+1)

9m+9n+9 = 14m-7n

-5m + 16n + 9 = 0

put m = 5n,

-5(5n) + 16n + 9 = 0

-25n + 16n + 9 = 0

-9n + 9 = 0

n = 1

m = 5, n = 1

Answer 2

Answer:

hope it helps........