Question 930051
1. {{{5x-y= 1}}}....eq.1
   {{{-5x+y=-3}}}....eq.2
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{{{5x-y= 1}}}....eq.1 solve for {{{y}}}

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

{{{-5x+5x-1=-3}}}....eq.2

{{{-cross(5x)+cross(5x)-1=-3}}}

{{{-1=-3}}}=> sins {{{-1=-3}}} is not true, there are no solutions and the system is inconsistent and lines are parallel


{{{ graph( 600, 600, -10, 10, -10, 10, 5x-1,5x-3) }}} 


2. {{{x+2y=-3}}}........eq.1
   {{{-3x+4y=-21}}}.......eq.2
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{{{x+2y=-3}}}........eq.1 solve for {{{x}}}

{{{x=-2y-3}}}......substitute in eq.2 

{{{-3(-2y-3)+4y=-21}}}.......eq.2 and solve for {{{y}}}

{{{6y+9+4y=-21}}}

{{{10y=-21-9}}}

{{{10y=-30}}}

{{{y=-30/10}}}

{{{y=-3}}}

go to {{{x=-2y-3}}} substitute {{{-3}}} for {{{y}}} and solve for {{{x}}}


{{{x=-2(-3)-3}}}

{{{x=-2(-3)-3}}}

{{{x=6-3}}}

{{{x=3}}}

intersection point is: ({{{3}}},{{{-3}}})


{{{ graph( 600, 600, -10, 10, -10, 10, (-1/2)x-3/2,(3/4)x-21/4) }}} 




3.  {{{2x+y=22}}}....eq.1
    {{{-8x+7y=0}}}....eq.2
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{{{2x+y=22}}}....eq.1  solve for {{{y}}}

{{{y=22-2x}}}...............substitute in eq.2

{{{-8x+7(22-2x)=0}}}....eq.2....... solve for {{{x}}}

{{{-8x+154-14x=0}}}

{{{154-22x=0}}}

{{{154=22x}}}

{{{154/22=x}}}

{{{x=7}}}

go to {{{y=22-2x}}} substitute {{{7}}} for {{{x}}} and solve for {{{y}}}

{{{y=22-2*7}}}

{{{y=22-14}}}

{{{y=8}}}

intersection point is: ({{{7}}},{{{8}}})


{{{ graph( 600, 600, -10, 15, -10, 15, 22-2x,(8/7)x) }}} 



4. {{{-8x+4y=-20}}}..........eq.1
    {{{x+y=10}}}.............eq.2
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{{{x+y=10}}}......eq.2 solve for {{{y}}}

{{{y=10-x}}}....substitute in eq.1


{{{-8x+4(10-x)=-20}}}..........eq.1...solve for {{{x}}}

{{{-8x+40-4x=-20}}}
{{{-12x+40=-20}}}

{{{20+40=12x}}}

{{{60=12x}}}

{{{60/12=x}}}

{{{x=5}}}

go to {{{y=10-x}}} plug in value for {{{x}}}

{{{y=10-5}}}

{{{y=5}}}

intersection point is: ({{{5}}},{{{5}}})


{{{ graph( 600, 600, -10, 15, -10, 15, 10-x,2x-5) }}}