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.

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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.