SOLUTION: Solve x+2y=3 and 5x+4y=8 by method of substitution. Show your work too

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Question 847854: Solve x+2y=3 and 5x+4y=8 by method of substitution. Show your work too
Answer by mxgirl22(39) About Me  (Show Source):
You can put this solution on YOUR website!

Solve by method of substitution. Show your work.

x%2B2y=3

5x%2B4y=8

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

Equation 1.) x%2B2y=3

Equation 2.) 5x%2B4y=8

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

Equation 1.) x%2B2y=3

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

Equation 1.)

x%2B2y=3

x%2B2y-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%2B4y=8

Equation 3.)x=3-2y


5%283-2y%29%2B4y=8 <------ I'm calling this Equation #4.

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

5%283-2y%29%2B4y=8

15-10y%2B4y=8

15-6y=8

15-15-6y=8-15

-6y=-7

-6y%2F-6=-7%2F-6

y=7%2F6

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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%2B2y=3

x%2B2%287%2F6%29=3

x%2B%287%2F3%29=3

x%2B%287%2F3%29-%287%2F3%29=3-%287%2F3%29

x=2%2F3

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Step 6.) Check using x=+2%2F3 and y=+7%2F6+.


Equation 2.)

5x%2B4y=8

5%282%2F3%29%2B4%287%2F6%29=8

%2810%2F3%29%2B4%287%2F6%29=8

%2810%2F3%29%2B%2814%2F3%29=8

24%2F3=8

8=8

Checks!

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Step 7.) Answer.

x=+2%2F3

y=+7%2F6+