Question 672213: The problem states, "Solve the system of equations using substitution method".
This is what I did so far...
x=3y -- equation 1
9x - 3y=12 -- equation 2
Step 1: Substitute x in equation 2 and solve
9x - 3y=12; x=3y
9(3y) - 3y=12
27y - 3y=12
24y=12
24y/24=12/24
y=1/2
Step 2: Substitute y in equation 1 and solve
x=3y
x=3/1(1/2)
x=3/2
Now, according to the answer key in my textbook, it states that there is no solution and that the lines are parallel. As you can see above, I somehow came up with a solution of (3/2, 1/2). Substituting (3/2, 1/2) into the original equations made them true (equal), not false (unequal). Please tell me where I went wrong with this problem.
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
The problem states, "Solve the system of equations using substitution method".
This is what I did so far...
x=3y -- equation 1
9x - 3y=12 -- equation 2
Step 1: Substitute x in equation 2 and solve
9x - 3y=12; x=3y
9(3y) - 3y=12
27y - 3y=12
24y=12
24y/24=12/24
y=1/2
Step 2: Substitute y in equation 1 and solve
x=3y
x=3/1(1/2)
x=3/2
Now, according to the answer key in my textbook, it states that there is no solution and that the lines are parallel. As you can see above, I somehow came up with a solution of (3/2, 1/2). Substituting (3/2, 1/2) into the original equations made them true (equal), not false (unequal). Please tell me where I went wrong with this problem.
x = 3y ---- eq (i)
9x – 3y = 12 ---- 3(3x – y) = 3(4) ------- 3x – y = 4 ------ eq (ii)
3(3y) – y = 4 ------ Substituting 3y for x in eq (ii)
9y – y = 4
8y = 4
y =  , or 
 ----- Substituting ˝ for y in eq (i)
 , or 
Your solution is correct!!
The answer you described, from the book, is INCORRECT, as the lines formed from the equations are NOT PARALLEL. Are you certain you’re looking at the right answer? When put in slope-intercept form, as seen below, the slopes are NOT EQUAL, thereby NOT PARALLEL, and thereby having a solution.
x = 3y ---- 3y = x -----  -----  ----- Slope, or 
9x - 3y = 12 ---- 3(3x – y) = 3(4) --- 3x – y = 4 --- - y = - 3x + 4 --- y = 3x – 4 --- Slope, or 
As seen above, the slopes are DIFFERENT
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