SOLUTION: x= 2y-1 and 2x+y=81 solve using substitution x=? y=? show work please thank you!!

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Question 38460This question is from textbook
: x= 2y-1 and 2x+y=81
solve using substitution
x=?
y=?
show work please thank you!! This question is from textbook

Found 2 solutions by Alwayscheerful, prabhjyot:
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
First step, plug x into the values of x
x=+2y-1
2%282y-1%29%2By=81
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=16.6.
  • Graphical form: Equation 2%2A%282y-1%29%2By=81 was fully solved.
  • Text form: 2*(2y-1)+y=81 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282y-1%29%2By=81+%29
    For tutors: simplify_cartoon( 2*(2y-1)+y=81 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2Ay-1%29%2By=highlight_red%28+81+%29.
Moved these terms to the left highlight_green%28+-81+%29
It becomes 2%2A%282%2Ay-1%29%2By-highlight_green%28+81+%29=0.
Look at highlight_red%28+2%2A%282%2Ay-1%29+%29%2By-81=0.
Expanded term 2 by using associative property on %282%2Ay-1%29
It becomes highlight_green%28+2%2A2%2Ay+%29-highlight_green%28+2%2A1+%29%2By-81=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2Ay-2%2A1%2By-81=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2Ay-2%2A1%2By-81=0.
Look at 4%2Ay-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2By-81=0.
Multiplied numerator integers
It becomes 4%2Ay-highlight_green%28+2+%29%2By-81=0.
Look at 4%2Ay-highlight_red%28+2+%29%2By-highlight_red%28+81+%29=0.
Added fractions or integers together
It becomes 4%2Ay%2Bhighlight_green%28+-83+%29%2By=0.
Look at 4%2Ay%2Bhighlight_red%28+-83+%29%2By=0.
Moved -83 to the right of expression
It becomes 4%2Ay%2By%2Bhighlight_green%28+-83+%29=0.
Look at 4%2Ay%2By%2Bhighlight_red%28+-83+%29=0.
Removed extra sign in front of -83
It becomes 4%2Ay%2By-highlight_green%28+83+%29=0.
Look at highlight_red%28+4%2Ay+%29%2Bhighlight_red%28+y+%29-83=0.
Eliminated similar terms highlight_red%28+4%2Ay+%29,highlight_red%28+y+%29 replacing them with highlight_green%28+%284%2B1%29%2Ay+%29
It becomes highlight_green%28+%284%2B1%29%2Ay+%29-83=0.
Look at %28highlight_red%28+4+%29%2Bhighlight_red%28+1+%29%29%2Ay-83=0.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ay-83=0.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ay+%29-83=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ay-83=0.
Look at highlight_red%28+5%2Ay-83+%29=0.
Solved linear equation highlight_red%28+5%2Ay-83=0+%29 equivalent to 5*y-83 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=16.6.

Universal Simplifier and Solver


Done!


y=highlight%2816.6%29
Plug y into the equation to find x
x=+2y-1
x=2%2816.6%29-1
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=32.2.
  • Graphical form: Equation x=2%2A%2816.6%29-1 was fully solved.
  • Text form: x=2*(16.6)-1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x=2%2A%2816.6%29-1+%29
    For tutors: simplify_cartoon( x=2*(16.6)-1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x=highlight_red%28+2%2A%28highlight_red%28+16.6+%29%29+%29-1.
Remove unneeded parentheses around factor highlight_red%28+16.6+%29
It becomes x=2%2Ahighlight_green%28+16.6+%29-1.
Look at x=highlight_red%28+2%2A16.6+%29-highlight_red%28+1+%29.
Replace constants in expression: highlight_red%28+2%2A16.6+%29,highlight_red%28+-1+%29 with highlight_green%28+32.2+%29
It becomes x=highlight_green%28+32.2+%29.
Look at x=highlight_red%28+32.2+%29.
Moved these terms to the left highlight_green%28+-32.2+%29
It becomes x-highlight_green%28+32.2+%29=0.
Look at highlight_red%28+x-32.2+%29=0.
Solved linear equation highlight_red%28+x-32.2=0+%29 equivalent to x-32.2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=32.2.

Universal Simplifier and Solver


Done!


x=highlight%2832.2%29
If you need more detailed explanations, you can see the lesson I wrote on substitution.
Hope this helps!

Answer by prabhjyot(165) About Me  (Show Source):
You can put this solution on YOUR website!
1x-2y = -1
2x+y = 81

Using Substitution Method.
Expressing x as a function of y (from the first equation) x = (-1 +2y)/1
Substituting this expression into the second equation:
2(-1-2y)/1+y = 81
Simplifying this expression:
5y = 83
or
y = 16.6
Now, substituting y = 16.6 back into the x expressed as a function of y:
x = (-1+2y)/1 = 32.2