How to solve a simple simultaneous equation

Solving simultaneous equations:


Example Question:

Equation 1 --->          2y – 4x = 2

Equation 2 --->          4y – 6x = 10


Find the unknown quantities, x and y.



Step 1: Firstly check whether there are more than 2 unknowns in the given question.

If there are more unknowns than given equations – the problem cannot be solved.


Step 2: Eliminate one unknown quantity by rearranging one of the equations such that x terms are on one side and the y terms are on the other side

Rearraging Equation 1:          y = 1 +2x     --->  (Equation 3)


Step 3: Substitute y (equation 3) into equation 2 - such that only one unknown quantity exists within the equation:

4y – 6x = 10

4 ( 1 + 2x) – 6x = 10

Expanding the above --->  4 + 8x – 6x =  10


Step 4: Bring x terms onto one side and numbers onto the other side:

8x - 6x = 10 - 4

2x = 6;

therefore x = 6/2=3



Step 5: Substitute x =3 into equation 1 or 2 to find the value of y

In this case, Equation 1 is chosen

2y – 4x = 2

2y – 4(3) = 2

2y – 12 = 2


y= 7


Final Answer: x=3; y=7







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