What this guide covers
Sec 2 N7 simultaneous linear equations and simple contextual formulation. Upper Secondary practice adds less familiar interpretation.
Choose the shorter valid method
If one pair of coefficients is equal and opposite, add the equations to eliminate that unknown. If an unknown is already isolated, substitute the whole expression into the other equation.
Eliminate a matching pair
Solve 2x+y=13 and x−y=2.
- Add the complete equations: 3x=15, so x=5.
- Use x−y=2: 5−y=2, giving y=3.
- The solution is (x,y)=(5,3).
Check: 2(5)+3=13 and 5−3=2; both originals hold.
Form the equations first
Two adult tickets and one child ticket cost $28. One adult and two child tickets cost $23. Find each ticket price.
- Let a and c be the prices in dollars. Then 2a+c=28 and a+2c=23.
- Double the second equation: 2a+4c=46. Subtract the first: 3c=18, so c=6.
- Then a+2(6)=23, so a=11.
Check: 2(11)+6=28 and 11+2(6)=23.
Check the pair
A proposed pair must satisfy both original equations. One matching equation alone is not enough.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
Solve x+y=11 and x−y=1.
Add to get 2x=12, so x=6 and y=5. Both equations check.
Solve y=3x−2 and x+y=14.
Substitute: x+3x−2=14, so x=4 and y=10. Check both originals: 10=3(4)−2 and 4+10=14.
Three pencils and one eraser cost $5; one pencil and one eraser cost $3. Find each price.
Let p,e be prices. 3p+e=5 and p+e=3. Subtract: 2p=2, so p=$1 and e=$2. Both totals check.
Where this connects
- See Sec 2 equation scope →
Connect this guide to linear inequalities, graphs and quadratic equations in the level map.
- Later: contextual equation challenge →
The Upper Secondary guide retains method choice and adds a more demanding interpretation task.
Sources and scope
Original Mentora examples and checks. Sec 2 N7 level placement follows the MOE G2/G3 Mathematics syllabus and the previously sampled Broadrick Sec 2 assessment; no school-paper wording is reproduced.