Question

for which values of p and q will the following pair of linear equations have infinitely many solutions ?

(p-1)x +3y =2
6x + (2-q)y =6

Answer 1

Answer:

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Step-by-step explanation:

An example of predicting the answer:

Think of a number.

Add 3.

Double that.

Subtract 4.

Cut that in half.

Subtract your original number.

Your result is 1!

Answer 2

Let (p-1) and (2-q) be 'm' and 'n' respectively.

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.Therefore, n = 9 and m = 2

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.Therefore, n = 9 and m = 2m = (p - 1) = 2 , p - 1 = 2

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.Therefore, n = 9 and m = 2m = (p - 1) = 2 , p - 1 = 2 p = 2+1 = 3

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.Therefore, n = 9 and m = 2m = (p - 1) = 2 , p - 1 = 2 p = 2+1 = 3n = (2 - q) = 9 , 2 - q = 9

Let (p-1) and (2-q) be 'm' and 'n' respectively.Therefore, mx + 3y = 2 (eq. 1) ; 6x + ny = 6 (eq. 2)The solutions can be infinite only if ny = (6 - 6x) and mx = (2 - 3y)As ny = (6 - 6x) = 3(2 - 2x) and 3y = (2 - mx) , ny = 3(3y) = 9y and mx = 2x.Therefore, n = 9 and m = 2m = (p - 1) = 2 , p - 1 = 2 p = 2+1 = 3n = (2 - q) = 9 , 2 - q = 9 2 - 9 = q = -7