Simultaneous Equations through Elimination

Being able to solve a pair of simultaneous equations through elimination is a key topic for GCSE students.   With the new criteria focusing more on problem solving and application of knowledge it is much less obvious for students when simultaneous equations is being assessed.

It’s important students are exposed to the types of questions they are likely to be asked in exams from as early as possible.   Plus, the problem solving questions are much more fun and rewarding to solve.

Setting up equations in the starter

Before students work with simultaneous equations they need to be confident with setting up and solving equations with one unknown.  This is why I use the question below as my starter.

simultaneous equations through elimination

Because the identical rectangles overlap by 7 cm students find it difficult to solve this intuitively and are therefore more likely to form some kind of equation as part of their working.  Generally, writing the equation  proves more challenging than solving it.

simultaneous equations through elimination

Introducing solving simultaneous equations through elimination

To transition into the development phase I ask the class how simultaneous equations are different to the ones they have seen previously.  ‘Because there are two unknowns’, eventually follows.

This leads nicely on to the key point of, for every unknown we need an equation.  So for two unknowns, x and y we need two equations involving both x and y.

We discuss coefficients and how to eliminate an unknown by either adding or subtracting the equations when coefficients are equal.  Students often find it difficult knowing when to add or subtract the equations to eliminate an unknown.  A quick recap of adding and subtracting with negatives and collecting like terms follows.

I work through the questions a) and b) as shown in the video and ask the class to work in pairs on question c).   Once they have shown me their working out on mini-whiteboards I feedback so students can attempt question d).

At this point we’re about 20 minutes into the lesson and the students can now start working independently either in pairs or individually.

simultaneous equations through elimination

I gather those who need a little more help and use the interactive Excel file to work through a couple more questions.

Differentiation for the most able

While the class are working through the problems I challenge the more able students to find an alternative method of solving the pair of simultaneous equations.  I encourage using the substitution method and ask the students to look out which method would be most suitable for different questions.

Assessing progress in the plenary

About 10 minutes before the end of the lesson we move on to the plenary.  This is an opportunity to introduce students to the type of question they are likely to be asked in their exams.  It always surprises me how intuitively some can derive the necessary equations.

simultaneous equations through elimination

Whenever possible I ask a student, or a pair, to demonstrate how they tackled the problem at the front of the class.  Those who have struggled are much more likely to engage with their peer at this point than having to listen to me again.


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