How to Solve Simultaneous Equations using Substitution Method

In South Africa, Grade 11 students learn about solving simultaneous equations using the substitution method in their Algebra curriculum. This method involves solving one equation for one variable and then substituting that value into the other equation.

To demonstrate, let's consider the following equations:

[ \begin{align*} x + y &= 10 \ 2x - y &= 5 \end{align*} ]

First, solve the first equation for (x) or (y). Let's solve it for (x):

[ x = 10 - y ]

Next, substitute (x) into the second equation:

[ 2(10 - y) - y = 5 ]

Solving for (y) gives us (y = 5). Then substitute (y) back into the first equation to solve for (x).

This method is an essential skill for Grade 11 learners and forms the foundation for more complex algebraic concepts.