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)   (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.

& .
You wish to use the substitution method.

Solve either equation for one of the variables.
Arbitrarily, x from the first equation:


-
Substitute for x in the second equation:

Solve this for y.




-----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:




-----again the right-member is an expression of constants.
Answer by MathTherapy(10552)   (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 = , or 



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!! 



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