What is solution by substitution?

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Simultaneous equations - Solution by substitution

As the variables (x & y) are the same in both equations, we can substitute from one equation into the other. This will give an equation with just one variable, which can easily be solved.


Equation 1   3y = 6x - 3

Equation 2   4y = 5x + 2

Make y the subject of equation 1, then substitute into equation 2:

·         Equation 1, divide both sides by 3 gives    y = 2x – 1

·         Equation 2, substitute for y from above gives  4(2x – 1) = 5x + 2

·         Multiply out brackets         8x – 4 = 5x + 2

·         Simplify and solve             3x = 6  therefore   x = 2

Substitute this value back into either of the original equations to solve for y:

Equation 1    3y = 6 (2) -3  therefore y = 3.

Key tip: Instead you could have made x the subject of an equation, and it can be either equation. Before you begin, think carefully about which variable will be easiest to make the subject of which equation.


Antonia M. A Level Chemistry tutor, A Level Maths tutor, GCSE Chemist...

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