SOLUTION: the line 2x+3y=1 intersects the curve x(x+y)=10 at A and B.Calculate the coordinates of A and of B.

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Question 9223: the line 2x+3y=1 intersects the curve x(x+y)=10 at A and B.Calculate the coordinates of A and of B.
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
From the first equation 2x+3y = 1, we get . Substitute it into the second equation

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=5,x=-6.
  • Graphical form: Equation was fully solved.
  • Text form: x*(x+(1-2x)/3)=10 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x*(x+(1-2x)/3)=10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Moved 1 to the right of expression
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-10+%29
It becomes .

Look at .
Expanded term x by using associative property on %28x%2B%28-2%2Ax%2B1%29%2F3%29
It becomes .

Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes .

Look at .
Expanded term x%2F3 by using associative property on %28-2%2Ax%2B1%29
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes .

Look at .
Eliminated similar terms highlight_red%28+x%5E2+%29,highlight_red%28+-x%5E2%2F3%2A2+%29 replacing them with highlight_green%28+%281-1%2F3%2A2%29%2Ax%5E2+%29
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F3+%29
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Equation highlight_red%28+x%5E2%2F3%2Bx%2F3-10=0+%29 is a quadratic equation: 0.333333333333333*x^2+0.333333333333333*x-10 =0, and has solutions 5,-6
It becomes .
Result:
This is an equation! Solutions: x=5,x=-6.

Universal Simplifier and Solver


Done!


x=5,-6
Substitute it into the first equation
x=5:
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (1-2x)/3 simplifies to -3
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (1-2x)/3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Replaced x with 5
It becomes .

Look at .
Replace constants in expression: highlight_red%28+1+%29,highlight_red%28+-2%2A5+%29 with highlight_green%28+-9+%29
It becomes .

Look at .
Removed extra sign in front of -9
It becomes .

Look at .
Removed extra sign in front of -3
It becomes .
Result:

Universal Simplifier and Solver


Done!


x=-6:
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (1-2x)/3 simplifies to 13/3
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (1-2x)/3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Replaced x with -6
It becomes .

Look at .
Replace constants in expression: highlight_red%28+1+%29,highlight_red%28+-2%2A-6+%29 with highlight_green%28+13+%29
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+13+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!


Answer: and

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