# The substitution method

**The substitution method**

Another method of solving simultaneous equation is by substituting one equation from another. For example:

*y* = 2*x* – 3 (equation a)

2*x* + 3*y* = 23 (equation b)

2*x* + 3(2*x* – 3) = 23 (substitute a into b, we know the equation for *y)*

2*x* + 6*x* – 9 = 23 (expand the brackets)

8*x* – 9 = 23 (simplify)

8*x* = 23 (add 9 to both sides)

*x* = 4 (divide both sides by 8)

To find the value of y, substitute the *x* = 4 into one of the equations:

*y* = 2*x* – 3 (*x* = 4)

*y* = 2 x 4 – 3

*y* = 8 – 3

*y* = 5

Point to note:

Equation a is arranged so that we know the what *y* is. If two equations are provide, to use this method, one of the equations should be re-arranged to make *y* the subject.