SOLUTION: Directions: Solve each system of equations by the substitution method. Problem: x+2y=6 & 2x+3y=8 Everytime I think I have it, im lost for the next problem, help!

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Question 885604: Directions: Solve each system of equations by the substitution method.
Problem: x+2y=6 & 2x+3y=8
Everytime I think I have it, im lost for the next problem, help!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
"Everytime I think I have it, im lost for the next problem, help!"

If that is the case, then try generalizing completely for two linear equations in standard form.

ax%2Bby=c & dx%2Bey=k.
You wish to use the substitution method.

Solve either equation for one of the variables.
Arbitrarily, x from the first equation:
ax=c-by
x=%28c-by%29%2Fa
-
Substitute for x in the second equation:
d%28c-by%29%2Fa%2Bey=k
Solve this for y.
d%28c-by%29%2Baey=ak
dc-bdy%2Baey=ak
-bdy%2Baey=ak-dc
y%28ae-bd%29=ak-dc
highlight%28y=%28ak-dc%29%2F%28ae-bd%29%29-----See that this solution for y uses only an expression of constants, so this will be evaluable when we know the values of those constants.
-
Again use the previous formula for x, substitute the found formula solution for y, and simplify:
x=%28c-by%29%2Fa
x=%28c-b%28%28ak-dc%29%2F%28ae-bd%29%29%29%2Fa
x=%28c%28ae-bd%29-b%28ak-dc%29%29%2F%28a%28ae-bd%29%29
x=%28ace-bcd-abk%2Bbcd%29%2F%28a%5E2e-abd%29
highlight%28x=%28ace-abk%29%2F%28a%5E2e-abd%29%29-----again the right-member is an expression of constants.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Directions: Solve each system of equations by the substitution method.
Problem: x+2y=6 & 2x+3y=8
Everytime I think I have it, im lost for the next problem, help!




2(6 - 2y) + 3y = 8 =------- Substituting 6 - 2y for x in eq (ii)

12 - 4y + 3y = 8

- 4y + 3y = 8 - 12

- y = - 4

y = %28-+4%29%2F-+1, or highlight_green%28highlight_green%284%29%29



Now, substitute 4 for y in either eq (i) or (ii) to determine the value of x. You should be able to do that.

Do a check after!! 



If you need a complete and detailed solution, let me know!!



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