Question

If (x2 - y2) = 10 and (x + y) = 2, find x and y.

Answer 1

Answer :

$\binom{( {x}^{2} - {y}^{2} ) = 10 }{(x + y) = 2} \\ \\ solve \: for \: x \\ \\ \binom{( {x}^{2} - {y}^{2}) }{x + y - y = 2 - y} \\ \\ \binom{( {x}^{2} - {y}^{2} )}{x = 2 - y} \\ \\ substitute \: the \: given \: value \: of \: x \: into \\ the \: equation \: {x}^{2} - {y}^{2} = 10$

$(2 - y) {}^{2} - {y}^{2} = 10 \\ \\ using \: \: (a - {b)}^{2} = {a}^2 - 2ab + {b}^{2} \\ expand \: the \: expression \\ \\ 4 - 4y + {y}^{2} - {y}^{2} = 10 \\ \\ 4 - 4y = 10 \\ \\ - 4y = 10 - 4 \\ \\ - 4y = 6 \\ \\ y = - \frac{6}{4} = - \frac{3}{2}$

$substitute \: the \: given \: value \: of \: y \: into \\ the \: equation \: x = 2 - y \\ \\ x = 2 - ( - \frac{3}{2} ) \\ \\ x = 2 + \frac{3}{2} \\ \\ x = \frac{7}{2} \\ \\ therefore \: x = \frac{7}{2} \: and \: y = - \frac{3}{2}$

Answer 2

Answer:

x = 3.5 ; y = -1.5

Step-by-step explanation:

Given Information:

• x² - y² = 10
• x + y = 2  ... ( 1 )

We know that,

⇒ a² - b² = ( a + b ) ( a - b )

⇒ x² - y² =  ( x + y ) ( x - y )

Substituting the known values we get,

⇒ 10 = 2 ( x - y )

⇒ x - y = 10/2 = 5 ... ( 2 )

Adding ( 1 ) and ( 2 )  we get,

⇒ x + y + x - y = 2 + 5

⇒ 2x = 7

⇒ x = 7/2 = 3.5

Substituting the value of x in ( 2 ) we get,

⇒ 3.5 + y = 2

⇒ y = 2 - 3.5 = -1.5

Hence value of x is 3.5 and value of y is -1.5

Hope it helped !!