SOLUTION: x+y=6 x+4y=3 using the substitution method. 2x-y=7 x+2y=1 using the addition method. Thanks!

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Question 841202: x+y=6 x+4y=3 using the substitution method.
2x-y=7 x+2y=1 using the addition method.
Thanks!

Answer by mxgirl22(39)   (Show Source): You can put this solution on YOUR website!

Problem #1.

Solve using the substitution method.




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1.) I'm going to label each equation in order to reference back to them.

Equation 1.)

Equation 2.)

---------------------------------
2.) Using equation #1 get "x" by itself.

Equation 1.)





---------------------------------
3.) Now that you have "x" by itself, plug in for equation 2. Solve for "y".









---------------------------------
4.) Now that you solved for "y", plug in in to equation 1.
Solve for "x".







---------------------------------
5.) Check and for either equation 1 or equation 2.

Equation 2.)






Checks!
---------------------------------
6.) Answer.

and


for Problem #1

--------------------------------------------------------------------------------
Problem #2.

Solve using the addition method.




---------------------------------
1.) I'm going to label each equation in order to reference back to them.

Equation 1.)

Equation 2.)

---------------------------------
2.) Both look easy to manipulate, but, if we use equation 2 we will have smaller numbers.

Equation 1.)

Equation 2.)

**First I'm going to get rid of the "x".

Equation 2.)


<-----Your "new" equation. I'll name it equation 3.



---------------------------------
3.) Using equation 1 & equation 3 combine.

Equation 1.)


Equation 3.)


***Notice: "2x" will be gone.

***** The "y" will now be -5y

******* And

******** The equation will now be <---I'm calling this equation 4.
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4.) Solve for "y" using equation 4.







--------------------------------------------------
5.) Using either equation 1 or equation 2, plug in to solve for "x".

Equation 1.)










--------------------------------------------------
6.) Check and for either equation 1 or equation 2.

Equation 2.)






Checks!

--------------------------------------------------
7.) Answer.

and

For Problem #2

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