Solving Linear Systems in MYP Year 5 Maths

What Is a Linear System?

A linear system (or system of simultaneous equations) involves two or more linear equations with the same variables. The solution is the set of values that satisfies all equations at the same time. In MYP Year 5, you work with systems of two equations in two unknowns.

Graphical Method

Graph both lines on the same set of axes. The point where they intersect is the solution. This method builds visual understanding and is useful for checking algebraic answers, but it depends on accuracy — use graph paper and plot at least three points per line.

Note: if the lines are parallel, there is no solution. If they are the same line, there are infinitely many solutions. Recognising these cases shows deeper understanding.

Algebraic Methods

Substitution

Rearrange one equation to isolate a variable, then substitute into the other. This method works well when one equation is already solved for x or y.

Elimination

Add or subtract the equations to eliminate one variable. You may need to multiply one or both equations by a constant first so that coefficients match. This method is often faster for equations with messy coefficients.

Checking Your Answer

Always substitute your solution back into both original equations to verify. This takes 30 seconds and can save marks if you made an arithmetic error.

Common Mistakes

• Substituting into the same equation you used to rearrange, instead of the other one.
• Sign errors when subtracting equations in the elimination method.
• Forgetting to find both variables — if you solve for x, you still need to find y.

Exam Application

Simultaneous equations appear in Criterion A problems requiring exact solutions and in Criterion D problems set in real contexts — for example, finding the price of two items or the break-even point of a business model. Make sure you can handle both types.