Question

if the system of equation 2x - 3 Y=3 and - 4 x + qY = p/2 is inconsistent which of the following cannot be the value of p​

Answer 1

The value of p can't be - 12 if the system of equations are inconsistent.

Given

System of equations

2x - 3y = 3

-4x + qy = p/2

The system of equations is inconsistent.

For the system to be inconsistent,

$\frac{2}{ - 4 } = \frac{ - 3}{q} \ne \frac{3}{ \frac{p}{2} }$

Solving for q

$\implies \frac{2}{ - 4 } = \frac{ - 3}{q} \\ \\ \implies 2q = - 4 \times - 3 \\ \\ \implies 2q = 12 \\ \\ \implies q = \frac{12}{2} = 6$

Solving for p

$\implies \frac{2}{ - 4 } \ne \frac{3}{ \frac{p}{2} } \\ \\ \implies \frac{1}{ - 2} \ne \frac{6}{p} \\ \\ \implies \: p \ne \: - 12$

Therefore, Value of p can't be - 12.

A system of equations in two variables,

ax + by = c, gx + fy = h

(1) has one solution and consistent, if

$\frac{a}{g} \ne \: \frac{b}{f}$

(2) has infinite solutions and consistent, if

$\frac{a}{g} = \: \frac{b}{f} = \frac{c}{h}$

(3) has no solutions and inconsistent if,

$\frac{a}{g} = \: \frac{b}{f} \ne \frac{c}{h}$

Answer 2

The value of p can't be - 12 if the system of equations are inconsistent.

Given

System of equations

2x - 3y = 3

-4x + qy = p/2

The system of equations is inconsistent.

For the system to be inconsistent,

−42 = q−3 ≠ 2p3

Solving for q

⟹ −42 = q−3

⟹2q=−4×−3

⟹2q=12

⟹q= 212

=6

Solving for p

⟹ −42 ≠ 2p3

⟹ −21 ≠ p6

⟹p≠−12

Therefore, Value of p can't be - 12.

A system of equations in two variables,

ax + by = c, gx + fy = h

(1) has one solution and consistent, if

ag ≠ bf

(2) has infinite solutions and consistent, if

ga = ch

(3) has no solutions and inconsistent if,

= ga≠ ch

= ga≠ ch