*Curriculum check:* ✓ Edexcel IGCSE ✓ OCR GCSE

## Solving simultaneous equations algebraically

**The best way to learn how to do this is to work through an example and practice yourself.**

**So off we go…**

**Solve:**

**2x = 6 – 4y**

**-3 – 3y = 4x**

**STEP 1: Label the equations**

**2x = 6 – 4y 1**

**-3 – 3y = 4x 2**

**STEP 2: Rearrange into ax + by = c**

**In equation 1: -4y becomes+4y**

** 2x + 4y = 6 1**

**In equation 2 : +4x becomes-4x**

**4x – 3 – 3y = 0 2**

**and -3 becomes+3**

** – 4x – 3y = 3 2**

**STEP 3: Multiply either or both equations to make either coefficient match**

**2x becomes 4x **

** 4x + 8y = 12 1 x 2**

**4x remains 4x **

** – 4x – 3y = 3 2**

**STEP 4: Add/subtract the 2 equations to get rid of the equivalent coefficients – in this case, we have a +4x and a -4x, so we need to add them to get to zero (+4 + -4 = 0)**

**1 + 2:**

**4x + 8y = 12 + – 4x – 3y = 3**

**To get: **

** 5y = 15**

**So: **

** y = 3**

**But this is only half of the solution – we need the x coordinate too – remember we are finding the point where the two equations cross each other.**

**STEP 5: Substitute in either of the original equations**

**Substitute y = 3 into the original equation 1 : 2x = 6 – 4y**

**To get: **

**2x = 6 – 4(3) **

**which is **

**2x =6 – 12**

** So: **

**x = -3**

**STEP 6: OUR SOLUTION**

**x = -3, y = 3 **