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  • Find the equation of the line passing through the point of intersection of 2x plus y is equal to 5 and x plus 3y plus 8 is equal to 0 and parallel to the line 3x plus 4y is equal to 7.

Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

Answers (1)

. Given 2x+y=5…. (1) and   x+3y=-8….(2)  

 Firstly, we find the point of intersection of both equations  we get y=-\frac{21}{5} and  x=\frac{23}{5}

  Hence, the point of intersection is \left (\frac{23}{5},-\frac{21}{5} \right )

  Now the slope of the equation 3x+4y=7  m=-\frac{3}{4} 

 Then the equation of the line passing through the point \left (\frac{23}{5},-\frac{21}{5} \right ) having slope -\frac{3}{4} is

 

 y-y1=m(x-x1) 

  y-\left ( -\frac{21}{5} \right )=-\frac{3}{4}\left ( x- \frac{23}{5} \right )

y+\frac{21}{5} =-\frac{3}{4} x+\frac{69}{20}

\frac{3}{4}x+y =\frac{69}{20} -\frac{21}{5}

\frac{3x+4y}{4} = -\frac{15}{5}

3x+4y+3=0

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