Question 840308

-4x+7y=-5
x-4y=-1
solve each system by substitution

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1.) Note: I'm going to label each equation.


Equation #1)  {{{-4x+7y=-5}}}
Equation #2)  {{{x-4y=-1}}}


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2.) Get "x" by itself in equation #2



Equation #2)
 

{{{x-4y=-1}}}
{{{x-4y+4y=-1+4y}}}
{{{x=-1+4y}}}


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3.) Now that we have "x" by itself in equation #2, plug in x=-1+4y into equation #1.


Equation #1)  
{{{-4x+7y=-5}}}


{{{-4(-1+4y)+7y=-5}}}


{{{4-16y+7y=-5}}}


{{{4-9y=-5}}}


{{{4-4-9y=-5-4}}}


{{{-9y=-9}}}


{{{-9y/-9=-9/-9}}}

{{{y=1}}}


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4.) Next, use the "y" value we found and plug in to either equation #1 or #2 to find "x" value.


Equation #1)  


{{{-4x+7y=-5}}}

{{{-4x+7(1)=-5}}}

{{{-4x+7=-5}}}

{{{-4x+7-7=-5-7}}}

{{{-4x=-12}}}


{{{-4x/-4=-12/-4}}}

{{{x=3}}}


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5.) Check using x=3 & y=1



Equation #2)  

{{{x-4y=-1}}}

{{{(3)-4(1)=-1}}}

{{{3-4=-1}}}

{{{-1=-1}}}


Checks!

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6.) Answer.


x=3
y=1