66. Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

4 Views | Posted 4 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 months ago

66. The given eqn of the line is.

4x + 7y – 3 = 0 _____ (1)

2x – 3y + 1 = 0 _______ (2)

Solving (1) and (2) using eqn (1) 2 x eqn (2) we get,

(4x + 7y – 3) 2 [ (2x – 3y + 1)] = 0

4x + 7y – 3 – 4x + 6y – 2 = 0

13y = 5

y = $\frac{5}{13}$

And 2x – 3 $(\frac{5}{13})$ + 1 = 0

2x = $\frac{15}{13}$ – 1 = $\frac{2}{13}$

$\Rightarrow x = \frac{1}{13}$

Point of intersection of (1) and (2) is $(\frac{1}{13}, \frac{5}{13})$

Since, the line passing through $(\frac{1}{13}, \frac{5}{13})$ has equal intercept say c then it is of the form

$\frac{x}{c} + \frac{y}{c} = 1 .$

x + y = c

$\Rightarrow \frac{1}{13} + \frac{5}{13} = c$

c = $\frac{6}{13}$

the read eqn of line is x + y = $\frac{6}{13}$

13x + 13y – 6 = 0

66. The given eqn of the line is.4x + 7y – 3 = 0 _____ (1)2x – 3y + 1 = 0 _______ (2)Solving (1) and (2) using eqn (1) 2 x eqn (2) we get, (4x + 7y – 3) 2 [ (2x – 3y + 1)] = 04x + 7y – 3 – 4x + 6y – 2 = 013y = 5y = <math><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math>And 2x – 3 <math><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> + 1 = 02x = <math><mrow><mfrac><mrow><mn>1</mn><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math> – 1 = <math><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math><math><mrow><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math>Point of intersection of (1) and (2) is <math><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac><mo>, </mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math>Since, the line passing through <math><mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac><mo>, </mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> has equal intercept say c then it is of the form<math><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>y</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo></mrow></math>x + y = c<math><mrow><mo>⇒</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac><mo>=</mo><mi>c</mi></mrow></math>c = <math><mrow><mfrac><mrow><mn>6</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math>the read eqn of line is x + y = <math><mrow><mfrac><mrow><mn>6</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math>13x + 13y – 6 = 0

0 Upvotes 0 Downvotes

66. Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question