Question

The number of solutions of the system of Equations given below is
$|x| + |y| = 1$
${x}^{2} + {y}^{2} = {a}^{2}$
$1 \div \sqrt{2} < a < 1$
$1) \infty$
2) 2
3) 4
4) 8​

Answer 1

Answer:

4) 8

Step-by-step explanation:

The equation

$|x| + |y| = 1$

can be written in 4 distinct equations which represents a rhombus.

Four equations are

$x + y = 1$

$- x + y = 1$

$- x - y = 1$

$x - y = 1$

And the equation x² + y² = a² represents a circle whose radius is 'a'

since

$\frac{1}{ \sqrt{2} } < a < 1$

$= > \frac{1}{2} < {a}^{2} < 1$

so the equation x² + y² = a² will cut the 4 equations at 8 points