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) About Me  (Show Source):
You can put this solution on YOUR website!

Problem #1.

Solve using the substitution method.

x%2By=6
x%2B4y=3

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

Equation 1.) x%2By=6

Equation 2.) x%2B4y=3

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

Equation 1.)

x%2By=6
x%2By-y=6-y
x=6-y

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3.) Now that you have "x" by itself, plug in x=6-y for equation 2. Solve for "y".

x%2B4y=3
%286-y%29%2B4y=3
6%2B3y=3
6-6%2B3y=3-6
3y=-3

3y%2F3=-3%2F3
y=-1
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4.) Now that you solved for "y", plug in y=-1 in to equation 1.
Solve for "x".

x%2By=6
x%2B%28-1%29=6
x-1=6
x-1%2B1=6%2B1
x=7

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5.) Check x=7 and y=-1 for either equation 1 or equation 2.

Equation 2.)

x%2B4y=3
%287%29%2B4%28-1%29=3
7-4=3
3=3

Checks!
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6.) Answer.

x=7 and y=-1


for Problem #1

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Problem #2.

Solve using the addition method.

2x-y=7
x%2B2y=1

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

Equation 1.) 2x-y=7

Equation 2.) x%2B2y=1

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

Equation 1.) 2x-y=7

Equation 2.) x%2B2y=1

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

Equation 2.)
x%2B2y=1
-2%28x%2B2y%29=-2%281%29
-2x-4y=-2 <-----Your "new" equation. I'll name it equation 3.



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3.) Using equation 1 & equation 3 combine.

Equation 1.) 2x-y=7


Equation 3.) -2x-4y=-2


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

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

******* And 7%2B%28-2%29=5

******** The equation will now be -5y=5 <---I'm calling this equation 4.
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4.) Solve for "y" using equation 4.

-5y=5

-5y%2F-5=5%2F-5

y=-1

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

Equation 1.)
2x-y=7
2x-%28-1%29=7
2x%2B1=7
2x%2B1-1=7-1
2x=6

2x%2F2=6%2F2

x=3

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6.) Check x=3 and y=-1 for either equation 1 or equation 2.

Equation 2.)
x%2B2y=1
%283%29%2B2%28-1%29=1
3-2=1
1=1


Checks!

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7.) Answer.

x=3 and y=-1

For Problem #2