Question

pls help me find the answer
will mark the best one as the brainliest​

Answer 1

Answer:

m = 5, n = 1

Step-by-step explanation:

Given Equations are:

(i)

3x + 4y = 12

Here a₁ = 3, b₁ = 4, c₁ = 12

(ii)

(m + n)x + 2(m - n)y - (5m - 1) = 0

Here a₂ = (m + n), b₂ = (2(m - n), c₂ = (5m - 1)

Given that the equation has infinite solutions.

∴  (a₁/a₂) = (b₁/b₂) = (c₁/c₂)

⇒ (3/m + n) = (4/2m - 2n) = (12/5m - 1)

(iii)

⇒ (3/m + n) = (4/2m - 2n)

⇒ 3(2m - 2n) = 4(m + n)

⇒ 6m - 6n = 4m + 4n

⇒ 2m = 10n

⇒ m = 5n

(iv)

(3/m + n) = (12/5m - 1)

⇒ 3(5m - 1) = 12(m + n)

⇒ 15m - 3 = 12m + 12n

⇒ 3m = 12n + 3

⇒ 3(5n) = 12n + 3

⇒ 15n = 12n + 3

⇒ n = 1

Substitute n = 1 in (iii), we get

⇒ m = 5n

⇒ m = 5

Thus, the values of m,n are 5,1

Hope it helps!