Singapore Math Drills Team · 4 November 2026
Free, distraction-free math drills aligned to the MOE syllabus. No sign-up needed to try.
Every inventor needs a lab. This one is a bedroom workbench under an angle-poise desk lamp, with a felt-tip blueprint taped to the wall. On the bench sits the invention: a cardboard box with arm holes, a slot for a mouth and five bottle-cap dials on its chest. The Mastermind, swim goggles pushed up on his red beanie, flips the cardboard power switch: "Power on." The dials start a slow, dim blink. "It thinks."
Then he pulls the box on over his hoodie. The robot is him. The invention has a name, "Project Brain Engine", and a plan: "Five questions a day." The Partner, lab assistant for the day, with a juice box in hand, is not convinced. "...Five?"
That is Project Brain Engine, the seventh episode of our comedy series, The Mastermind, and our second Secondary episode. Watch it first (it is under a minute), then read on. The secret inside this robot is a Secondary 2 puzzle.
Every question card that goes into the robot's mouth slot gets a full-intensity "Beep." from inside the box, and one more dial glows steady. On the fifth beep, the chest panel stamped TOP SECRET creaks open on two equations: x + y = 10 and x − y = 4. "Add them." The +y and the −y are struck out, and the working runs down to x = 7, y = 3. The Partner sums up the invention: "The robot is you. Doing five questions."
He has a point. And the move on that chest panel is one of the most useful ideas in Secondary 2 math.
A single equation such as x + 3 = 10 has one unknown, and your child already knows how to undo it. A pair of simultaneous equations has two unknowns, and neither equation is enough on its own. x + y = 10 is true for 7 and 3, but also for 6 and 4, and for infinitely many other pairs. Only one pair makes both equations true at the same time. That is what "simultaneous" means.
In the MOE teaching sequence, simultaneous linear equations come in Sec 2 for G2 and G3 Mathematics, and later, in upper secondary, for G1 Mathematics. If you are not sure which subject level your child takes, our guide to G1, G2 and G3 Mathematics explains the difference.
Children used to "getting x on its own" often cannot see where to start, and once they find one letter, it is tempting to stop there. One idea fixes both: make one letter disappear.
Teachers call this the elimination method. Write the two equations one above the other, with the x terms lined up and the y terms lined up. Then:
+y and −y, add the equations. If they match, such as +y and +y, subtract one equation from the other.The rule fits in one line: opposite signs, add; same signs, subtract. Either way, the aim is a line with only one letter on it. When neither letter lines up, as in 2x + y = 8 and x + 3y = 9, the next step is to multiply one equation first so that a pair does. The idea stays the same.
Solve x + y = 10 and x − y = 4.
Step 1: Look at y. It is +y in the first equation and −y in the second. Opposite signs, so add.
Step 2: Add the equations, left side to left side and right side to right side. On the left, (x + y) + (x − y) = 2x, because +y and −y cancel. On the right, 10 + 4 = 14. So 2x = 14.
Step 3: Solve. x = 14 ÷ 2 = 7.
Step 4: Substitute. Put x = 7 into the first equation: 7 + y = 10, so y = 3.
Step 5: Check in both equations. 7 + 3 = 10 ✓ and 7 − 3 = 4 ✓. The answer is x = 7, y = 3.
Step 5 matters more than it looks. We found y from the first equation, so 7 + 3 = 10 was bound to work. The second equation is the real test, and it is the check on the Mastermind's panel: 7 − 3 = 4.
One of the practice cards in the episode reads "Solve y = 2x, x + y = 9".
The first equation already says what y is: twice x. So swap y for 2x in the second equation. This is the substitution method, usually the shortest route when one letter is already on its own.
Step 1: Substitute. x + y = 9 becomes x + 2x = 9.
Step 2: Solve. 3x = 9, so x = 3.
Step 3: Find y. y = 2x = 2 × 3 = 6.
Step 4: Check in both equations. 6 = 2 × 3 ✓ and 3 + 6 = 9 ✓. The answer is x = 3, y = 6.
At the school bookshop, 2 pens and 1 notebook cost $7, and 1 pen and 1 notebook cost $5. How much does a pen cost, and how much does a notebook cost?
Step 1: Write the equations. Let a pen cost p dollars and a notebook cost n dollars. Then 2p + n = 7 and p + n = 5.
Step 2: Look at n. It is +n in both equations. Same signs, so subtract the second equation from the first: (2p + n) − (p + n) = p, and 7 − 5 = 2. So p = 2.
Step 3: Substitute. Put p = 2 into the second equation: 2 + n = 5, so n = 3.
Step 4: Check in the equation you did not use. We found n from the second equation, so check the first: 2 × 2 + 3 = 7 ✓. A pen costs $2 and a notebook costs $3.
The words explain the subtraction: the first set has one more pen than the second and costs $2 more, so one pen costs $2.
2p + n = 7 and p + n = 5 gives 3p + 2n = 12: still two letters. If nothing disappears, try the other operation.(2p + n) − (p + n), the right sides must be subtracted too: 7 − 5, not 7 + 5.(x + y) − (x − y) is 2y, not 0, because taking away −y adds y. Brackets around each equation keep the signs in view.Two cups and a handful of bottle caps, buttons or coins are enough.
While your child looks away, split 10 bottle caps between two cups. Then give two clues: "There are 10 caps altogether, and the left cup has 4 more than the right cup." Your child writes the clues as equations, L + R = 10 and L − R = 4, and adds them: 2L = 14, so L = 7 and R = 3. Then lift the cups and count. Lifting the cups is the check.
Swap roles each round and change the numbers. Choose a total and a difference that are both even or both odd, so the caps split into whole numbers. Five rounds is plenty, one for each dial.
Make one house rule for every pair your child solves, at home or in homework: check in the equation you did not use. If y came from the first equation, the check goes in the second. A wrong pair can fit one equation, but never both, so this check catches the slip.
Keep each session short and stop while your child still wants to play. When your child is stuck, ask "Which letter can disappear?" before "What is the answer?", and praise the method rather than the speed.
In the episode, the whole secret programme is five questions a day, each one logged with a "Beep." and a steady dial, while the day counter goes Day 1, Day 7, Day 30. It only ever goes up. Simultaneous equations become comfortable the same way: one idea, met often and checked every time.
That is the idea we built Singapore Math Drills around:
Simultaneous Linear Equations is one of the Secondary 2 topics in our collection, alongside Algebraic Expansion & Factorisation and Congruence & Similarity, the other two parts on the episode's blueprint. Three of the episode's practice cards, such as "Factorise x² − 9", come from Algebraic Expansion & Factorisation.
The Mastermind stays in the box to the very end, all five dials glowing steady. Told that the robot is just him, he whispers back, eyes front: "Robots don't talk."
Try a free interactive Secondary 2 worksheet and see how calm practice feels, with no signup or credit card required.