Simultaneous Linear Equations (Sec 2) Practice
Solve pairs of simultaneous linear equations using substitution and elimination methods. Translate word problems into two-variable systems and interpret solutions graphically. A major O-Level topic.
Common Mistakes to Avoid
Using elimination when coefficients don't align β scale them first
In substitution, substituting into the same equation you derived the subject from
Arithmetic errors when adding/subtracting equations in elimination
Practice Questions
Try each question. When you're stuck, reveal the Socratic strategy β a guided hint that teaches you how to think, not just what to write.
Solve: x + y = 10 and x β y = 2.
Solve: y = 2x and 3x + y = 15.
Two numbers sum to 20 and their difference is 4. Find the numbers.
Parent & Tutor Insight
Simultaneous equations are one of those topics where students make most of their errors in arithmetic, not concept. Encourage neat layout: write each equation numbered, and label each step. Examiners award method marks even for wrong numerical answers.
Want More Practice?
Get personalised daily practice questions at your exact level. Adaptive questions, Socratic hints, and progress tracking β all free to start.
No credit card required Β· MOE 2026 Aligned Β· Free to start
Common Questions
When should I use elimination vs substitution?
Use elimination when one variable has the same (or easily scaled) coefficient in both equations β it is usually faster. Use substitution when one variable is already isolated or has a coefficient of 1 (e.g. y = 3x + 1). With practice, you'll recognise which is faster at a glance.
What does it mean graphically if simultaneous equations have no solution?
The two equations represent parallel lines (same gradient, different y-intercept). They never intersect, so there is no common (x, y) solution. Algebraically, you'll get a contradiction like 0 = 5.
Can simultaneous equations have infinitely many solutions?
Yes β if both equations represent the same line (one is a multiple of the other). Algebraically, you'll get a tautology like 0 = 0. This means every point on the line is a solution.