MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Consistency of Linear System of Equations

Solve the fol...

Question

Solve the following equation.
$x^{2} y^{2} - 2 x + y^{2} = 0, 2 x^{2} - 4 x + 3 + y^{3} = 0$ .

Open in App

Solution

The given system of equations is equivalent to $y^{2} = 2 x / (1 + x^{2}), 2 (x - 1)^{2} + 1 + y^{3} = 0$ .
Since $2 x / (1 + x^{2}) \leq 1$ for all real x, it follows from the first of these equations that $y^{2} \leq 1$ or $- 1 \leq y \leq 1$ .
Again from the second equation of the system, we get
$y^{3} = - 1 - 2 (x - 1)^{2} \leq - 1$
Now since $y \leq - 1$ and $y \geq - 1$ , we must have $y = - 1$
Then $x = 1$ . This the solution is $x = 1$ , $y = - 1$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Solve the following equations:

6 x^{4} + x^{2} y^{2} + 16 = 2 x (12 x + y^{3}), x^{2} + x y - y^{2} = 4

Q. Solve the following equations:

3 x + y - 2 z = 0

,

4 x - y - 3 z = 0

,

x^{3} + y^{3} + z^{3} = 467

Q. Solve the following differential equation:

\sqrt{1 + x^{2} + y^{2} + x^{2} y^{2}} + x y \frac{d y}{d x} = 0

Q. Solve the following equations:

x^{2} y^{2} + 400 = 41 x y, y^{2} = 5 x y - 4 x^{2}

.

Q. Solve the following equations:

\frac{x^{3} + y^{3}}{(x + y)^{2}} + \frac{x^{3} - y^{3}}{(x - y)^{2}} = \frac{43 x}{8}, 5 x - 7 y = 4

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Consistency of Linear System of Equations

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon