SOLUTION: hi, my name is julie and i'm trying to find out how to do this problem, it is: x = 1/3y + 2 -2x - y = 1 the answers that are representing x and y have to have t

Algebra ->  Algebra  -> Equations -> SOLUTION: hi, my name is julie and i'm trying to find out how to do this problem, it is: x = 1/3y + 2 -2x - y = 1 the answers that are representing x and y have to have t      Log On

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Question 44893: hi, my name is julie and i'm trying to find out how to do this problem, it is:
x = 1/3y + 2
-2x - y = 1
the answers that are representing x and y have to have the same numbers that can be plugged into them.
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+y%2F3+%2B+2
x+-+y%2F3+=+2

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+-0.333333333333333%5Cy+=+2%2C%0D%0A++++-2%5Cx+%2B+-1%5Cy+=+1+%29%0D%0A++We'll use substitution. After moving -0.333333333333333*y to the right, we get:
1%2Ax+=+2+-+-0.333333333333333%2Ay, or x+=+2%2F1+-+-0.333333333333333%2Ay%2F1. Substitute that
into another equation:
-2%2A%282%2F1+-+-0.333333333333333%2Ay%2F1%29+%2B+-1%5Cy+=+1 and simplify:
EXPLAIN simplification of an expression
Your Result:
Simplify -2*(2/1--0.333333333333333*y/1)+-1y=1
Your Answer:
  • Solutions: y=-3.
  • Graphical form: Equation -2%2A%282%2F1--0.333333333333333%2Ay%2F1%29%2B-1y=1 was fully solved.
  • Text form: -2*(2/1--0.333333333333333*y/1)+-1y=1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-2%2A%282%2F1--0.333333333333333%2Ay%2F1%29%2B-1y=1+%29
    simplify_cartoon( -2*(2/1--0.333333333333333*y/1)+-1y=1 )

Detailed explanation:

Look at -2%2A%282%2Fhighlight_red%28+1+%29--0.333333333333333%2Ay%2F1%29%2B-1%2Ay=1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes -2%2A%282--0.333333333333333%2Ay%2F1%29%2B-1%2Ay=1.
Look at -2%2A%282--0.333333333333333%2Ay%2Fhighlight_red%28+1+%29%29%2B-1%2Ay=1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes -2%2A%282--0.333333333333333%2Ay%29%2B-1%2Ay=1.
Look at -2%2A%28highlight_red%28+2+%29--0.333333333333333%2Ay%29%2B-1%2Ay=1.
Moved 2 to the right of expression
It becomes -2%2A%28--0.333333333333333%2Ay%2Bhighlight_green%28+2+%29%29%2B-1%2Ay=1.
Look at -2%2A%28--0.333333333333333%2Ay%2B2%29%2B-1%2Ay=highlight_red%28+1+%29.
Moved these terms to the left highlight_green%28+-1+%29
It becomes -2%2A%28--0.333333333333333%2Ay%2B2%29%2B-1%2Ay-highlight_green%28+1+%29=0.
Look at -highlight_red%28+2%2A%28--0.333333333333333%2Ay%2B2%29+%29%2B-1%2Ay-1=0.
Expanded term -2 by using associative property on %28--0.333333333333333%2Ay%2B2%29
It becomes highlight_green%28+2%2A-0.333333333333333%2Ay+%29-highlight_green%28+2%2A2+%29%2B-1%2Ay-1=0.
Look at 2%2A-0.333333333333333%2Ay-highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2B-1%2Ay-1=0.
Multiplied numerator integers
It becomes 2%2A-0.333333333333333%2Ay-highlight_green%28+4+%29%2B-1%2Ay-1=0.
Look at 2%2A-0.333333333333333%2Ay-highlight_red%28+4+%29%2B-1%2Ay-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes 2%2A-0.333333333333333%2Ay%2Bhighlight_green%28+-5+%29%2B-1%2Ay=0.
Look at 2%2A-0.333333333333333%2Ay%2Bhighlight_red%28+-5+%29%2B-1%2Ay=0.
Moved -5 to the right of expression
It becomes 2%2A-0.333333333333333%2Ay%2B-1%2Ay%2Bhighlight_green%28+-5+%29=0.
Look at 2%2A-0.333333333333333%2Ay%2B-1%2Ay%2Bhighlight_red%28+-5+%29=0.
Removed extra sign in front of -5
It becomes 2%2A-0.333333333333333%2Ay%2B-1%2Ay-highlight_green%28+5+%29=0.
Look at highlight_red%28+2%2A-0.333333333333333%2Ay+%29%2Bhighlight_red%28+-1%2Ay+%29-5=0.
Eliminated similar terms highlight_red%28+2%2A-0.333333333333333%2Ay+%29,highlight_red%28+-1%2Ay+%29 replacing them with highlight_green%28+%282%2A-0.333333333333333%2B-1%29%2Ay+%29
It becomes highlight_green%28+%282%2A-0.333333333333333%2B-1%29%2Ay+%29-5=0.
Look at %28highlight_red%28+2%2A-0.333333333333333+%29%2Bhighlight_red%28+-1+%29%29%2Ay-5=0.
Replace constants in expression: highlight_red%28+2%2A-0.333333333333333+%29,highlight_red%28+-1+%29 with highlight_green%28+-1.66666666666667+%29
It becomes %28highlight_green%28+-1.66666666666667+%29%29%2Ay-5=0.
Look at %28highlight_red%28+-1.66666666666667+%29%29%2Ay-5=0.
Removed extra sign in front of -1.66666666666667
It becomes %28-highlight_green%28+1.66666666666667+%29%29%2Ay-5=0.
Look at highlight_red%28+%28-highlight_red%28+1.66666666666667+%29%29%2Ay+%29-5=0.
Remove unneeded parentheses around factor highlight_red%28+1.66666666666667+%29
It becomes -highlight_green%28+1.66666666666667+%29%2Ay-5=0.
Look at highlight_red%28+-1.66666666666667%2Ay-5+%29=0.
Solved linear equation highlight_red%28+-1.66666666666667%2Ay-5=0+%29 equivalent to -1.66666666666667*y-5 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
Solutions: y=-3.

Done!
So, we know that y=-3. Since x+=+2%2F1+-+-0.333333333333333%2Ay%2F1, x=1.

Answer: system%28+x=1%2C+y=-3+%29.