# How do you find two numbers whose difference is 4 and the difference of their square is 88?

$x = 13$
$y = 9$

#### Explanation:

How do you find two numbers whose difference is 4 and the difference of their square is 88?

Solution:

let $x =$the larger number
let $y =$the smaller number

$x - y = 4$first equation
${x}^{2} - {y}^{2} = 88$second equation

Substitute the first in to the second equation

${x}^{2} - {y}^{2} = 88$second equation
${\left(y + 4\right)}^{2} - {y}^{2} = 88$
${y}^{2} + 8 y + 16 - {y}^{2} = 88$
$8 y = 88 - 16$
$8 y = 72$
$y = 9$

Solve for $x$ using first equation

$x - y = 4$first equation
$x - 9 = 4$
$x = 9 + 4$
$x = 13$

God bless... I hope the explanation is useful.