An equation of a straight line passing through the $$inter-section$$ of the straight lines $$3x$$ – $$4y$$ $$+$$ $$1$$ $$=$$ $$0$$ and $$5x$$ $$+$$ y – $$1$$ $$=$$ $$0$$ and making $$non-zero$$, equal intercepts on the axes is

Question

An equation of a straight line passing through the $$inter-section$$ of the straight lines $$3x$$ – $$4y$$ $$+$$ $$1$$ $$=$$ $$0$$ and $$5x$$ $$+$$ y – $$1$$ $$=$$ $$0$$ and making $$non-zero$$, equal intercepts on the axes is

Infinity Learn · Accepted Answer

Equation of any line through the point of intersection of the given lines is (3x$$−$$4y+1)+k(5x+y$$−$$1)=0or$$ $$(3+5k)x+(k$$−$$4)y+1$$−$$k=0or$$ $$x(k$$−$$1)/(3+5k)+y(k$$−$$1)/(k$$−$$4)=1Since$$ $$x-intercept$$ $$=$$ $$y-intercept$$⇒k−$$13+5k=k$$−$$1k$$−$$4$$ ⇒ $$(k$$−$$1)(3+5k$$−$$k+4)=0$$⇒ $$k=1$$ or $$k=$$−$$7/4For$$ k $$=$$ $$1$$, $$(1) becomes $$8x$$ – $$3y$$ $$=$$ $$0$$ which makes zero intercepts on the axes.∴ $$k=$$−$$7/4$$ ⇒ The required equation $$is4(3x$$−$$4y+1)$$−$$7(5x+y$$−$$1)=0$$⇒$$23x+23y=11$$.

An equation of a straight line passing through the inter-section of the straight lines $3 x - 4 y + 1 = 0$ and $5 x + y - 1 = 0$ and making non-zero, equal intercepts on the axes is

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An equation of a straight line passing through the inter-section of the straight lines 3x – 4y + 1 = 0 and 5x + y – 1 = 0 and making non-zero, equal intercepts on the axes is

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An equation of a straight line passing through the inter-section of the straight lines $3 x - 4 y + 1 = 0$ and $5 x + y - 1 = 0$ and making non-zero, equal intercepts on the axes is