Solving 3xy²+x³=9 And 3x²y+y³=18 | Complex Simultaneous Equations
How to Solve Complex Simultaneous Equations where X and Y are of degree 3 (Polynomial) and there are More than two X and Y. Then X and Y Multiply both in equation 1 and equation 2.
Example, Solve the Simultaneous Equation Question 3xy²+x³=9 and 3x²y+y³=18. Looking at the question, we obviously can’t eliminate or use the elimination method. We also cannot do Substitution by making x or y subject formular.
OTHERS ARE LOVING A. BEST APPS FOR JAMB, WAEC, NCEE, IJMB AND BECE B. FREE VIDEOS FOR BECE, JAMB, WAEC AND POST UTME
You may want to quickly go through my post on the 7 Types of Simultaneous Equation questions to expect in any exam by clicking here or simply continue reading for the solution to 3xy²+x³=9 and 3x²y+y³=18.
How to Solve 3xy²+x³=9 And 3x²y+y³=18
Step 1: Label the equations
3xy²+x³=9 ….. 1
3x²y+y³=18 ….. 2
Step 2: Add Equation 1 and Equation 2
3xy² + x³ + 3x²y + y³ = 27
x³ + 3xy² + 3x²y + y³ = 27 ….. 3
Step 3: Simplify the Equation
Recall that (x + y)³ = x³ + 3xy² + 3x²y + y³. Substituting this into Equation 3, we have that
(x + y)³ = 27
x + y = ∛27
∴ x + y = 3 …. *
Step 4: Subtract Equation 1 from Equation 2
3x²y – 3xy² + y³ – x³ = 9
y³ – 3xy² + 3x²y – x³ = 9 …. 4
Recall that (y – x)³ = y³ – 3xy² + 3x²y – x³. Substituting this into Equation 3, we have that
(y – x)³ = 9
y – x = ∛9
∴ y – x = 2.08 …. **
Step 5: Rearrange and Solve equation * and equation **
x + y = 3 …. 5
– x + y = 2.08 … 6
Step 6: Add equation 5 and 6
2y = 5.08 and y = 2.54
Step 7: Substitute the value of y (y=2.54) in equation 6
– x + 2.54 = 2.08
-x = 2.08 – 2.54
-x = -0.46
∴ x = 0.46
Step 8: Bring out the solution
The Solution to the Simultaneous Equations 3xy²+x³=9 and 3x²y+y³=18 is y = 2.54 and x = 0.46
That’s all. You have successfully solved the Simultaneous equation. Feel free to let me know how you feel using the comment box below and don’t fail to share this article with your friends using the share buttons.
RECOMMENDED
WHAT ELSE DO YOU WANT?
- SEARCH FLASH LEARNERS
- COMPLETE JAMB GUIDE
- ABOUT BECE, WAEC AND NECO
- VACANCIES AND JOBS GUIDE
- LATEST NIGERIA SCHOOL NEWS
- ACADEMIC AND CAREER GUIDE
- SCHOLARSHIPS AND INTERNSHIPS
- SPECIAL TOPICS FOR PARENTS
- How To Test Yourself After Reading A Jamb Or Waec Topic - Jan 14, 2021
- NECO 2021 Syllabus And Topics For All Subjects - Jan 14, 2021
- How To Pass Waec 2021 Without Expo Or Runs - Jan 14, 2021
Comments
Solving 3xy²+x³=9 And 3x²y+y³=18 | Complex Simultaneous Equations — No Comments
HTML tags allowed in your comment: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>