Question

Find the coordinates of the intersection of the lines $2x-3y+1=0$ and $2x+4y+5=0$.

• A. ($\frac{19}{14}$, $\frac{4}{7}$)
• B. ($\frac{-19}{14}$, $\frac{4}{7}$)
• C. ($\frac{19}{14}$, $\frac{-4}{7}$)
• D. ($\frac{-19}{14}$, $\frac{-4}{7}$)

Answer 1

The correct option is D

($\frac{-19}{14}$, $\frac{-4}{7}$)

$2x-3y+1=0$ - - - - - (1)

$2x+4y+5=0$ - - - - - (2)

Equation (1) can be written as $2x-3y=-1$ - - - - - (3)

Equation (2) can be written as $2x+4y=-5$ - - - - - (4)

(3) - (4) $⟹$ $-7y=4$ $⟹$ $y=\frac{-4}{7}$

Substituting $y=\frac{-4}{7}$ in equation (3),

$2x-3\left(\frac{-4}{7}\right)=-1$

$⟹2x+\frac{12}{7}=-1$

$⟹2x=-1-\frac{12}{7}$

$⟹x=\frac{-19}{14}$

$\therefore$ The coordinates of the intersection of the lines $2x-3y+1=0$ and $2x+4y+5=0$ are ($\frac{-19}{14}$, $\frac{-4}{7}$).