Back to the full dot-point answer
NSWMaths Standard 2Quick questions
Year 12: Algebra
Quick questions on Simultaneous linear equations for HSC Maths Standard 2
11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is what "simultaneous" means?Show answer
Two linear equations in and each describe a straight line. The simultaneous solution is the pair where both equations are satisfied at the same time. Graphically, that is the point where the two lines cross.
What is algebraic method 1?Show answer
Use when one equation is already solved for one variable, or can be quickly rearranged.
What is algebraic method 2?Show answer
Use when the coefficients line up neatly, or can be matched by multiplying through.
What is graphical method?Show answer
Plot both lines on the same axes. Read off the intersection point. The HSC will sometimes give you a pre-drawn graph and ask you to read the solution from it. Always state coordinates as a pair .
What is practical modelling?Show answer
Worded problems usually compare two situations: two phone plans, two taxi fares, two energy providers, two job offers. The strategy is:
What is elimination?Show answer
Solve and .
What is phone plan comparison (Australian example, 2025 retail rates)?Show answer
Plan A: \25\ per call. Plan B: \15\ per call.
What is forgetting to substitute back?Show answer
You found but the question wants the pair . Always solve for both.
What is wrong sign on elimination?Show answer
When the coefficients match (not opposite), you must subtract, not add. Slow down and check.
What is misreading a graphical intersection?Show answer
Read coordinates carefully. The HSC often picks intersection points at convenient values like , not .
What is answering the equation rather than the question?Show answer
A taxi problem wants "after km, both fares are \18.67x = 6.67, y = 18.67$". :::