Question 753944
{{{ x+y=5}}}.....eq.1 

{{{y=x^2-25}}}......eq.2
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{{{ x+y=5}}}.....eq.1...solve for {{{y}}}

{{{ y=-x+5}}}....eq.1a.......substitute in eq.2


{{{y=x^2-25}}}......eq.2

{{{-x+5=x^2-25}}}.....solve for {{{x}}}

{{{0=x^2+x-5-25}}}

or {{{x^2+x-30=0}}}.....write {{{x}}} as {{{6x-5x}}}

{{{x^2+6x-5x-30=0}}}....group

{{{(x^2+6x)-(5x+30)=0}}}

{{{x(x+6)-5(x+6)=0}}}

{{{(x-5)(x+6)=0}}}......use zero product rule to find solutions

if {{{x-5=0}}} => {{{x=5}}}

if {{{x+6=0}}} => {{{x=-6}}}

now find {{{y}}}

if  {{{highlight(x=5)}}} => {{{ y=-5+5}}}=> {{{ highlight(y=0)}}}

if  {{{highlight(x=-6)}}} => {{{ y=-(-6)+5}}}=> {{{ y=6+5}}} => {{{ highlight(y=11)}}}


{{{drawing (600, 600, -15, 15, -30, 15,locate(5,-0.2,A(5,0)),locate(-6,10.8,B(-6,11)),graph(600, 600, -15, 15, -30, 15, -x+5, x^2-25)) }}}