If the three lines 2x + y = 4,3x + 2y = 3,and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For three lines to be concurrent,the determinant of their coefficients must be zero. The system of equations is: $2x + y - 4 = 0$ $3x + 2y - 3 = 0

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) For three lines to be concurrent,the determinant of their coefficients must be zero. The system of equations is: $2x + y - 4 = 0$ $3x + 2y - 3 = 0$ $ax + 3y - 2 = 0$ The condition for concurrency is: $\begin{vmatrix} 2 & 1 & -4 \ 3 & 2 & -3 \ a & 3 & -2 \end{vmatrix} = 0$ Expanding the determinant along the first row: $2(2(-2) - (-3)(3)) - 1(3(-2) - (-3)(a)) - 4(3(3) - 2(a)) = 0$ $2(-4 + 9) - 1(-6 + 3a) - 4(9 - 2a) = 0$ $2(5) + 6 - 3a - 36 + 8a = 0$ $10 + 6 - 36 + 5a = 0$ $-20 + 5a = 0$ $5a = 20$ $a = 4$

If the three lines $2x + y = 4$,$3x + 2y = 3$,and $ax + 3y = 2$ are concurrent,find the value of $a$.

Similar Questions

The equation of the line passing through the point of intersection of the lines $3x - 2y - 1 = 0$ and $x - 4y + 3 = 0$ and the point $(\pi, 0)$ is:

The equation of the line passing through the intersection of the lines $x - y = 4$ and $3x + y = 7$ and parallel to the line $x + 2y = 1$ is:

If the lines $4x + 3y = 1$,$y = x + 5$,and $5y + bx = 3$ are concurrent,then the value of $b$ is:

The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

Find the equation of the line passing through the intersection of the lines $x + y - 3 = 0$ and $2x - y + 1 = 0$ and the point $(2, -3)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module