Question

(v) Find the value of m such that the following system of linear equations has infinite number of solutions.

mx + 4y = m - 4 , 16x + my = m

Answer 1

Answer:

m value is 4 because +4-4=0. 1_6into 4

Answer 2

Answer:

Value of m = 8 for the equation to have infinite solutions

Step-by-step explanation:

We have,

mx + 4y = m - 4 , 16x + my = m

OR

mx + 4y - (m - 4) = 0 , 16x + my - m = 0

a1x + b1y + c1 = 0, a2x + b2y + c2 = 0

Then,

a1 = m, a2 = 16

b1 = 4, b2 = m

c1 = -(m - 4), c2 = -m

We know that,

IF (a1/a2) = (b1/b2) = (c1/c2)

then it will have infinite solutions

So,

(m/16) = (4/m) = -(m - 4)/(-m)

Let's take

(m/16) = (4/m)

Cross multiplying,

m × m = 16 × 4

m² = 64

m = √64

m = +8 or -8

Now, Let's check the second equality,

(4/m) = -(m - 4)/(-m)

(4/m) = (m - 4)/m

Cross multiplying,

4m = m(m - 4)

4m = m² - 4m

m² - 4m - 4m = 0

m² - 8m = 0

m(m - 8) = 0

So,

m = 0 or m = 8

Since,

From first and second equality we got m = 8 as a common value.

Value of m = 8 for the equation to have infinite solutions

Hope it helped you and believing you understood it...All the best