Question 902317
 

here you have system to solve; you can do it by substitution, by elimination, or by graphing

{{{x - y = 5}}}............eq.1

 {{{x * y = 8}}}..........eq.2
________________________________________let's use substitution

start with {{{x - y = 5}}}............eq.1 and solve it for {{{y}}}

{{{x - 5 = y}}}............substitute in eq.2

{{{x * (x-5) = 8}}} ..........solve it for {{{x}}}

{{{x^2-5x = 8}}}

{{{x^2-5x -8=0}}}....use quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (- (-5) +- sqrt( (-5)^2-4*1* (-8)))/(2*1) }}}


{{{x = (5 +- sqrt( 25+32))/2 }}}

{{{x = (5 +- sqrt( 57))/2 }}}

{{{x = (5 +- 7.6)/2 }}}

solutions:

{{{x = (5 + 7.6)/2 }}}

{{{x = 12.6/2 }}}

{{{x = 6.3 }}}

or

{{{x = (5 - 7.6)/2 }}}

{{{x = -2.6/2 }}}

{{{x = -1.3 }}}


now find {{{y}}}

{{{x - y = 5}}}............eq.1...if {{{x = 6.3 }}}


{{{6.3 - 5 = y}}} 


{{{1.3 = y}}} 


and

{{{x - y = 5}}}............eq.1...if {{{x = -1.3 }}}


{{{-1.3 - 5 = y}}} 


{{{-6.3 = y}}} 


so, one pair of solutions is:

{{{x = 6.3 }}} and {{{1.3 = y}}} 

the other is

{{{x = -1.3 }}} and {{{-6.3 = y}}} 


check:


{{{x * y = 8}}} ..........eq.2..plug in {{{x = 6.3 }}} and {{{1.3 = y}}}

 
{{{6.3 * 1.3 = 8}}}

{{{8.19 = 8}}} ...round to whole number

{{{8= 8}}}
 
{{{x * y = 8}}} ..........eq.2..plug in {{{y = -6.3 }}} and {{{-1.3 = x}}}

 
{{{-1.3 * (-6.3) = 8}}}

{{{8.19 = 8}}} ...round to whole number

{{{8= 8}}}