Question

Given the pair of equations
ax +(a –1)y=1 and (a +1)x – ay=1
For which one of the
following values of 'a', there
is no common solution of
the given pair of equations?​

Answer 1

Answer:

+sqrt (1/2) and -sqrt(1/2) are the values for which there will be no solutions of the equations. refer the ratio of the coordinates

Answer 2

Answer:

a = 1/√2

Step-by-step explanation:

There are several situations that can be mathematically represented by two equations that are not linear to start with. But we allow them so that they are reduced to a pair of linear equations.

• Consistent system. A system of linear equations is said to be consistent if it has at least one solution.

• Inconsistent system. A system of linear equations is said to be inconsistent if it has no solution.

CONDITIONS FOR CONSISTENCY

Let the two equations be:

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Then,

Relationship between    Graph           Number of               Consistency                                                                                                                              

coeff. or the pair of                               Solutions

equations

 

a1/a2≠b1/b2         Intersecting lines   Unique solution Consistent

a1/a2=b1/b2≠c1/c2 Parallel lines           No solution    Inconsistent

a1/a2=b1/b2=c1/c2  Co-incident lines   Infinite solutions Consistent

Now, in the given equations we have,

a/(a+1) = (a - 1)/ -a

On cross multiplying,

-a² = (a + 1) (a - 1)

-a² = a² - 1      [ (a + b) (a - b) = a² - b²]

-a² - a² = -1

-2 a² = -1

a ² = 1/2

a = √1/2 = 1/√2

Thus, a = 1/√2