Question

The equation of straight line passing through the intersection of the lines $x - 2 y = 1$ and $x + 3 y = 2$ and parallel to $3 x + 4 y = 0$ is.

• A. $3 x + 4 y + 5 = 0$
• B. $3 x + 4 y - 10 = 0$
• C. $3 x + 4 y - 5 = 0$
• D. $3 x + 4 y + 6 = 0$

Answer 1

Answer: (C)

$3 x + 4 y - 5 = 0$

Answer 2

The intersection point of lines $x - 2 y = 1$ and $x + 3 y = 2$ is $\left( \frac { 7 } { 5 } , \frac { 1 } { 5 } \right)$ and the slope of required line $= - \frac { 3 } { 4 }$

∴ Equation of required line is $y - \frac { 1 } { 5 } = \frac { - 3 } { 4 } \left( x - \frac { 7 } { 5 } \right)$

⇒$\frac { 3 x } { 4 } + y = \frac { 21 } { 20 } + \frac { 1 } { 5 }$⇒ $3 x + 4 y = 5$ ⇒$3 x + 4 y - 5 = 0$.

⇒$\frac { 3 x } { 4 } + y = \frac { 21 } { 20 } + \frac { 1 } { 5 }$⇒ $3 x + 4 y = 5$ ⇒$3 x + 4 y - 5 = 0$