Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
941 views
in Linear Equations by (56.3k points)

Solve the following system of equations:

1/(2x) + 1/(3y) = 2; 

1/(3x) + 1/(2y) = 13/6

1 Answer

0 votes
by (30.5k points)
selected by
 
Best answer

Let 1/x = u and 1/y = v, 

So the given equations becomes, 

u/2 + v/3 = 2 ………………(i) 

u/3 + v/2 = 13/6 ……………(ii) 

From (i), we get 

u/2 + v/3 = 2 

⇒ 3u + 2v = 12 

⇒ u = \(\frac{(12 – 2v)}{3}\) ………….(iii)

Using (iii) in (ii) 

[(12 – 2v)/3]/3 + \(\frac{v}{2}\) = \(\frac{13}{6}\) 

\(\frac{(12 – 2v)}{9 }\)+ v/2 = \(\frac{13}{6}\) 

⇒ 24 – 4v + 9v = (\(\frac{13}{6}\)) x 18 [after taking LCM] 

⇒ 24 + 5v = 39 

⇒ 5v = 15 

⇒ v = 3 

Substituting v in (iii) 

u = \(\frac{(12 – 2(3))}{3}\)

⇒ u = 2 

Thus, x = \(\frac{1}{u}\)

⇒ x = \(\frac{1}{2}\) and y = \(\frac{1}{v}\) 

⇒ y = \(\frac{1}{3}\) 

The solution for the given pair of equations is x = \(\frac{1}{2}\) and y = \(\frac{1}{3}\) respectively.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...