Chapter 11.6, Problem 26AYU

In Problems 25-54, solve each system. Use any method you wish.

$\{\begin{array}{l}{x}^2-y^2\text{ = 21}\\ x\text{ + }y\text{ = 7}\end{array}$

To determine

To solve: The given system of equation.

Answer to Problem 26AYU

Solution:

$\left(\frac{35}{2}, -\frac{21}{2}\right)$

Explanation of Solution

Given:

$x^2 - y^2 = 21$   -----(Eq 1)

$x + y = 7$   -----(Eq 2)

Calculation:

Substituting $y = 7 - x$ in Eq 1 we get

$x^2 - {\left(7 - x\right)}^2 = 21$

The above equation can be rewritten as

$\begin{array}{lll}14x - 70\hfill & = \hfill & 0\hfill \\ 2x - 35\hfill & = \hfill & 0\hfill \end{array}$

$x = 35/2$

Substituting $x$ in Eq 2, we get $y = - 21/2$

The solutions to the equations is $\left(\frac{35}{2}, -\frac{21}{2}\right)$.