# 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.

Example:

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.

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