Year 10 - Simultaneous equations - Free practice

Year 10 Simultaneous Equations Worksheets

Substitution, elimination, graphical - all three methods.

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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.

About this worksheet

Why we built it

Simultaneous equations are one of the most-tested Year 10 topics. These worksheets give your student practice on all three solution methods - substitution, elimination, graphical - plus applied problems that need the student to set up the system before solving.

What's covered

Sub-skills your student will practise

  • Solving by substitution
  • Solving by elimination
  • Solving graphically (intersection of two lines)
  • Recognising no solution / infinite solutions
  • Word problems requiring setup of two equations

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Frequently asked

Questions parents ask about simultaneous equations

What are simultaneous equations?

Two or more equations that students need to solve together to find values that satisfy all of them. Most Year 10 work is two equations with two variables (x and y).

What are the three solution methods?

Substitution (solve one equation for one variable, then sub into the other), elimination (add or subtract the equations to cancel a variable), and graphical (sketch both lines and find the intersection).

Which method should students use?

Substitution if one equation is already 'y = ...' or 'x = ...'. Elimination if the coefficients line up neatly. Graphical when the question specifically asks for it or as a quick check.

When do simultaneous equations have no solution?

When the two lines are parallel (same gradient, different y-intercept). When they're the same line (same gradient and y-intercept), there are infinitely many solutions. Year 10 expects students to recognise both cases.

Want a real plan for the term?

Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.

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