How to teach simultaneous equations and inequalities
Year 10 (ages 15 to 16)
Simultaneous equations are two equations sharing the same two variables, solved together to find the one pair of values that satisfies both. Linear inequalities are solved much like equations, with one extra rule when multiplying or dividing by a negative.
How to teach it
- Start with simple simultaneous equations already set up for elimination, like x + y = 10 and x - y = 4, adding them to cancel y.
- Show that once one variable is found, substituting it back into either original equation finds the second.
- Extend to equations that need scaling first before a variable cancels, choosing whichever variable eliminates more simply.
- Introduce inequalities as 'solve like an equation', then add the one exception: flip the inequality sign when multiplying or dividing by a negative number.
- Have students verify simultaneous solutions by substituting into BOTH original equations, not just one.
Worked example
Solve x + y = 10 and x - y = 4 Add the equations: 2x = 14, so x = 7 Substitute into x + y = 10: 7 + y = 10, so y = 3
Common mistakes
- Substituting the found value into only one equation and assuming the answer is fully checked.
- Adding the equations when subtracting (or vice versa) would actually eliminate a variable.
- Forgetting to flip the inequality sign when multiplying or dividing both sides by a negative number.
- Treating an inequality's solution as a single value rather than a whole range of values.
Frequently asked questions
What does it mean to solve simultaneous equations?
It means finding the one pair of values (x and y) that makes BOTH equations true at the same time. Graphically, this is the point where the two lines cross.
How do you solve simultaneous equations by elimination?
Add or subtract the two equations to eliminate one variable, leaving a single equation in the other variable to solve. Then substitute that value back into either original equation to find the second variable.
How do you solve a linear inequality like an equation?
Solve it the same way as an equation, undoing operations in reverse order on both sides, except that multiplying or dividing by a NEGATIVE number reverses the inequality's direction.
What year are simultaneous equations and inequalities taught?
In the Australian Curriculum, this is a Year 10 skill: AC9M10A01 covers expanding, factorising and solving, AC9M10A02 covers inequalities and simultaneous equations specifically, extending into modelling growth and decay (AC9M10A04) and exploring functions (AC9M10A05).
Practise with free worksheets
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