Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Test of Mathematics Solution Subjective 62 - System of Equations

Test of Mathematics at the 10+2 Level

This is a Test of Mathematics Solution Subjective 62 (from ISI Entrance).

The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.


Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

Problem

Consider the system of equations x + y = 2, ax + y = b. Find conditions on a and b under which
(i) the system has exactly one solution;
(ii) the system has no solution;
(iii) the system has more than one solution.

Solution

Key Idea

Solution to the linear equations

\( a_{11} x + a_{12} y = b_1 \\ a_{21} x + a_{22} y = b_2 \)

\(a_{11} \times a_{22} - a_{12} \times a_{21} \neq  0  \) implies there is a unique solution.

\(a_{11} \times a_{22} - a_{12} \times a_{21} = 0  \) implies there is either no solution or infinitely many solution.

No solution if: \( \frac{a_{11}}{a_{21} } = \frac{a_{12}}{a_{22}} \neq = \frac{b_1}{b_2}  \); infinitely many solutions other wise.

i

 

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com