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.

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.

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