Free Year 10 Maths Inequalities & Simultaneous Equations Worksheet

This worksheet teaches students to solve linear inequalities and simultaneous linear equations in two variables, and interpret the solution as the intersection point of two lines in a real-world context. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.

The concepts it covers:

• Solving a linear inequality uses the same steps as solving an equation, except the inequality sign flips when multiplying or dividing both sides by a negative number.
• Simultaneous linear equations in 2 variables can be solved by substitution (replace one variable using the other equation) or elimination (add/subtract multiples of the equations to cancel a variable).
• The solution to a pair of simultaneous linear equations is the point (x,y) where their two graphed lines intersect — it satisfies both equations at once.
• Two lines with the same gradient but different y-intercepts are parallel and never intersect — the system has no solution.
• Two equations that are exact multiples of each other represent the same line — the system has infinitely many solutions.

What your child will practise:

• Solving a linear inequality, correctly flipping the sign when needed.
• Solving simultaneous linear equations using substitution.
• Solving simultaneous linear equations using elimination, scaling equations as needed to match coefficients.
• Verifying a simultaneous-equation solution by substituting it back into both original equations.
• Formulating a real-world scenario as a pair of simultaneous equations, solve it, and interpret the result in context.

Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.