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Question

Find the equation of the line passing through the point of intersection of the lines4x7y3=0 and 2x3y+1=0 that has equal intercepts on the axes.

Solution
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Let the equation of the line having equal intercepts on the axes be

xa+ya=1

x+y=a....(1)
On solving equation 4x+7y3=0 and 2x3y+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

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