Question 847854

Solve by method of substitution. Show your work.


{{{x+2y=3}}}


{{{5x+4y=8}}}


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Step 1.) I like to label each equation, so I'm going to do that now.


Equation 1.) {{{x+2y=3}}}


Equation 2.) {{{5x+4y=8}}}


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Step 2.) I can see that Equation #1 is going to be easier to manipulate.


Equation 1.) {{{x+2y=3}}}


**Get "x" by itself in Equation #1.


Equation 1.) 


{{{x+2y=3}}}


{{{x+2y-2y=3-2y}}}


{{{x=3-2y}}}     <------ I'm calling this Equation #3.


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Step 3.) Using Equation #3, plug in to Equation #2.


**Note:


Equation 2.){{{5x+4y=8}}}


Equation 3.){{{x=3-2y}}}



{{{5(3-2y)+4y=8}}}   <------ I'm calling this Equation #4.


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Step 4.) Solve for "y", using equation #4.


{{{5(3-2y)+4y=8}}}


{{{15-10y+4y=8}}}


{{{15-6y=8}}}


{{{15-15-6y=8-15}}}


{{{-6y=-7}}}


{{{-6y/-6=-7/-6}}}


{{{y=7/6}}}


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Step 5.) Using the value we got for "y" in step 4, plug in to either Equation #1 or Equation #2.



Equation 1.)


{{{x+2y=3}}}


{{{x+2(7/6)=3}}}


{{{x+(7/3)=3}}}


{{{x+(7/3)-(7/3)=3-(7/3)}}}


{{{x=2/3}}}


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Step 6.) Check using {{{x= 2/3}}} and {{{y= 7/6 }}}.



Equation 2.)


{{{5x+4y=8}}}


{{{5(2/3)+4(7/6)=8}}}


{{{(10/3)+4(7/6)=8}}}


{{{(10/3)+(14/3)=8}}}


{{{24/3=8}}}


{{{8=8}}}


Checks!


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Step 7.) Answer.


{{{x= 2/3}}} 


{{{y= 7/6 }}}