Question

(I) for what value p will the following system of equations has no solution
(2p-1)x + (p-1)y=2p+1;
y+3x - 1 =0​

please answer me immediately

Answer 1

✪ANSWER✪

• p = 2

★EXPLAINATION★

☆GIVEN☆

System of linear equations in x and y

(2p-1)x+(p-1)y = 2p +1

3x + y - 1 = 0

☆TO FIND☆

• Value of p for no solution.

✵CONCEPT✵

System of linear equation in two variable

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

has no solution if

$\frac{a₁}{a₂} = \frac{b₁}{b₂} ≠\frac{c₁}{c₂}$

᯽CALCULATION᯽

For no solution of the given sustem of equations

(2p-1)x+(p-1)y = 2p +1

3x + y = 1

$\frac{2p-1}{3} = \frac{p-1}{1} ≠\frac{2p+1}{1}$

$⇒2p-1 =3(p-1), p-1 ≠2p+1$

$⇒2p-1 =3p-3, -1-1 ≠2p-p$

$⇒3-1 =3p-2p, -2 ≠2p-p$

$⇒p =2, p ≠ -2$

$⇒p =2$