Find the equation of the line passing through the point of intersection of the lines4x−7y−3=0 and 2x−3y+1=0 that has equal intercepts on the axes.
Let the equation of the line having equal intercepts on the axes be
xa+ya=1
x+y=a....(1)
On solving equation 4x+7y−3=0 and 2x−3y+1=0 we obtain x=113andy=513
∴{113,513} is the point of intersection of the two given lines.
Since equation (1) passes through point {113,513}
{113+513}=a
⇒a=613
∴ Equation (1) becomes x+y=613,i.e.,13x+13y=6
Thus the required equation of the line is 13x+13y=6