Question

solve :- 2u +v=7/3 uv, u+3v= 11/3uv​

Answer 1

Answer:

Answer

Clearly, the given equations are not linear equations in the variables u and v but can be reduced to linear equations by appropriate substitution.

If we put u=0 in either of the two equations, we get v=0.

So, u=0,v=0 form a solution of the given system of equations.

To find the other solutions, we assume that u



=0,v



=0.

Now, u



=0,v



=0⇒uv



=0.

On dividing each one of the given equations by uv, we get

v

6

+

u

3

=7 (i)

v

3

+

u

9

=11 (ii)

Taking

u

1

=x and

v

1

=y, the given equations become

3x+6y=7 ..(iii)

9x+3y=11 .(iv)

Multiplying equation (iv) by 2, the given system of equations becomes

3x+6y=7 .(v)

18x+6y=22 .(vi)

Substracting equation (vi) from equation (v), we get

−15x=−15⇒x=1

Putting x=1 in equation (iii), we get

3+6y=7⇒y=

6

4

=

3

2

Now, x=1⇒

u

1

=1⇒u=1

and, y=

3

2

⇒

v

1

=

3

2

⇒v=

2

3

.

Hence, the given system of equations has two solutions given by