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# Test of Mathematics Solution Subjective 62 - System of Equations  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  implies there is a unique solution. implies there is either no solution or infinitely many solution.

No solution if: ; infinitely many solutions other wise.

i 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  implies there is a unique solution. implies there is either no solution or infinitely many solution.

No solution if: ; infinitely many solutions other wise.

i

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