LCHL Simultaneous Equations - Exam Solutions

A look into the two ways in which Simultaneous Equations are asked at Leaving Cert level, using past Exam Questions as examples.
Both are a step up from Junior Cert Simultaneous Equations, on which I have done two videos, links below:

JCHL Simultaneous Equations:

Quick Maths - Simultaneous Equations:

Another explanation from Brian McLogan:

Key Points:
*For all simultaneous equations, organising your question (labelling your equations, giving yourself enough space, etc. is so important*

In a set of simultaneous equations where you have 3 equations and 3 variables (x, y, and z, for example), you will have to:

1. Choose which variable you want to eliminate. Pick the variable whose coefficients have the “easiest” Lowest Common Multiple with the coefficients of the same variable in your other two equations.
2. Eliminate the variable using two of your equations.
3. Eliminate the same variable using a DIFFERENT pair of your original equations.
4. You will be left with two equations, with two variables (essentially like a Junior Cert Simultaneous Equation Question)
5. Using your two new equations, combine them to eliminate one of your variables.
6. Once you have found the value of your first variable, substitute it back into one of your equations from step 4.
7. Finally, substitute the two values you now have back into one of your original equations (from the question) to find your last variable.

Well done, you did it!

In a set of simultaneous equations where you have 2 variables (x and y, for example), and 2 equations (where on of them has x squared, or y squared, or “xy”) and you will have to:

1. Isolate the x (or y, whichever is easier) in the equation that does NOT deal with the x squared, y squared, or “xy”.
2. Substitute your answer into your equation that DOES have the x squared, y squared, or “xy”.
3. Simplify and get your answers. Be careful with squaring fractions and negative numbers. Chances are you may simplify down to a quadratic. Know your Guide Number method OR your quadratic formula (link to both of these are below) The majority of the time there will be two different values for x.
4. Substitute your values for x into one of your original equations to get the corresponding y value.
You should have two sets of answers at the end.

Well done, you did it!

The Quadratic Formula:

Factorising a Quadratic Equation (Guide Number Method):

[mrluddenmaths]

0:17 Into to LCHL Simultaneous Equations
3:07 2014 Paper 1, Q 4 (3 Equations, 3 Variables)
22:42 2014 Paper 1, Q4 Marking Scheme
24:07 Key Points (3 Equations, 3 Variables)
24:45 2016 Paper 1, Q2(b)
47:32 2016 Paper 1, Q2(b) Marking Scheme
49:28 Overview of Exam Q's from 2013, 2018, and 2012 (with Marking Schemes)
51:29 Key Points