SOLUTION: Please help! Could you tell me if I made a mistake in this problem and if I did, where? 3x + y = 6 x − 2y = 2 y = 6 − 3x x − 2(6 − 3x) = 2 x −

Algebra ->  Systems-of-equations -> SOLUTION: Please help! Could you tell me if I made a mistake in this problem and if I did, where? 3x + y = 6 x − 2y = 2 y = 6 − 3x x − 2(6 − 3x) = 2 x −      Log On


   

Question 631430: Please help! Could you tell me if I made a mistake in this problem and if I did, where?
3x + y = 6
x − 2y = 2
y = 6 − 3x
x − 2(6 − 3x) = 2
x − 12 − 6x = 2
−5x − 12 = 2
+12 +12
x = −2.8
3(−2.8) + y = 6
−8.4 + y = 6
+8.4 +8.4
y = 14.4
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

3x + y = 6  ⇒   y = 6 − 3x   |yes, good work

 x − 2y = 2 

x - 2(6 - 3x) = 2    | Careful... %28-2%29%28-3x%29 = + 6x

 x -12 + 6x = 2 

   7x = 14

    x = 2   and y = 0   6-3%2A2

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
3x + y = 6
x − 2y = 2
solve for y in the first equation to get:
y = 6 − 3x
substitute for y in the second equation to get:
x − 2(6 − 3x) = 2
simplify to get:
x − 12 − 6x = 2 *********
this i where you went wrong.
the simplified equation should be equal to:
x - 12 + 6x = 2
when you multiply -2 * -3x you get a + 6x, not a - 6x.
the rest of the processing would go like this:
x - 12 + 6x = 2
combine like terms to get:
7x - 12 = 2
add 12 to both sides to get:
7x = 14
divide both sides by 7 to get:
x = 2
first original equation is 3x + y = 6
substitute 2 for x to get 3(2) + y = 6
simplify to get 6 + y = 6
subtract 6 from both sides of the equation to get y = 0
your answer should be:
x = 2
y = 0
substitute these values into the second original equation.
second original equation is:
x − 2y = 2
substitute 2 for x and 0 for y to get:
2 - 2(0) = 2 which simplifies to 2 = 2
this confirms the values for x = 2 and y = 0 are good.