For what value of p does the system of equations 2x – py = 0,3x + 4y

1.	For what value of p does the system of equations 2x – py = 0,3x + 4y = 0 has non zero solution ? A) p = -6B) p = -8/3C) p = -2/3D) p = 6
Answer» Correct option is (B) p = -8/3 Given system of equations is 2x – py = 0 __________(1) 3x + 4y = 0 __________(2) Multiply equation (1) by 3 & equation (2) by 2, we obtain 6x - 3py = 0 __________(3) and 6x+8y = 0 __________(4) Subtract equation (3) from (4), we get (6x+8y) - (6x - 3py) = 0 - 0 = 0 \(\Rightarrow\) (8+3p)y = 0 for non-zero solution (i.e., \(y\neq0),\) 8+3p = 0 \(\Rightarrow\) \(p=\frac{-8}3\) Hence, for \(p=\frac{-8}3,\) the given system of equations has non zero solution. Correct option is B) p = -8/3

For what value of p does the system of equations 2x – py = 0,3x + 4y = 0 has non zero solution ? A) p = -6B) p = -8/3C) p = -2/3D) p = 6

Answer»

Correct option is (B) p = -8/3

Given system of equations is

2x – py = 0 __________(1)

3x + 4y = 0 __________(2)

Multiply equation (1) by 3 & equation (2) by 2, we obtain

6x - 3py = 0 __________(3)

and 6x+8y = 0 __________(4)

Subtract equation (3) from (4), we get

(6x+8y) - (6x - 3py) = 0 - 0 = 0

\(\Rightarrow\) (8+3p)y = 0

for non-zero solution (i.e., \(y\neq0),\)

8+3p = 0

\(\Rightarrow\) \(p=\frac{-8}3\)

Hence, for \(p=\frac{-8}3,\) the given system of equations has non zero solution.

Correct option is B) p = -8/3