Chapter SH, Problem 9.19EP

To determine

To find: the solution of the system of equation.

Answer to Problem 9.19EP

The equation will be satisfied at point $\left(\text{±5,±2}\right)$

Explanation of Solution

Given:

  ${\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}\text{=21}$ .

  ${\text{y}}^{\text{2}}{\text{+x}}^{\text{2}}\text{=29}$ .

Concept used:

Addition and elimination method are used to solve the two unknown variables having two equation.

In additions method the two equation will sum up and eliminating method two equation will subtract.

Calculation:

  ${\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}\text{=21}$ ........... $\left(\text{i}\right)$

  ${\text{y}}^{\text{2}}{\text{+x}}^{\text{2}}\text{=29}$ ...........…. $\left(\text{ii}\right)$

Adding given equation $\left(\text{i}\right)$ and $\left(\text{ii}\right)$ :

  ${\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}{\text{+y}}^{\text{2}}{\text{+x}}^{\text{2}}\text{=21+29}$ .

  ${\text{2x}}^{\text{2}}\text{=50}$ .

  ${\text{x}}^{\text{2}}\text{=}\frac{\text{50}}{2}=25$ .

  $\text{x=}\pm \sqrt{25}$ .

  $\text{x=}\pm 5$ .

By putting the value $\text{x=}\pm 5$ in equation $\left(\text{i}\right)$ :

At $\text{x=5}$ :

  $5^{\text{2}}{\text{-y}}^{\text{2}}\text{=21}$ .

  $\text{y=}\pm \text{2}$ .

At $\text{x=-5}$ .

  ${\left(-5\right)}^{\text{2}}{\text{-y}}^{\text{2}}\text{=21}$ .

  $\text{y=}\pm \text{2}$ .

Hence, at the value of $\left(\text{±5,±2}\right)$ the equation satisfied.