A system of equations asks for values that satisfy several equations at once. This chapter of SPM Additional Mathematics has four linked skills, and each ends with a check against every original equation.
What does this chapter cover?
The skills build on each other. Every lesson uses substitution or elimination, so read the method-choice lesson early.
| Skill | Question it answers |
|---|---|
| Three linear equations in three unknowns | How do I reduce three unknowns to two, then one? |
| One linear and one nonlinear equation | How do I substitute into a squared or product equation? |
| Choosing substitution or elimination | Which method keeps the algebra short? |
| Rejecting invalid solutions | Which answers make sense in the situation? |
How do the skills connect?
One small example shows the link. Solve x + y = 5 and x² + y² = 13.
The first equation is linear, so write y = 5 − x and substitute: x² + (5 − x)² = 13, which gives 2x² − 10x + 12 = 0, or x² − 5x + 6 = 0. Then x = 2 or 3, so the pairs are (2, 3) and (3, 2).
Both pairs satisfy both equations. In a word problem, a condition such as “length is greater than width” can rule out one pair. That check is the last skill in the chapter.
Where should I start?
Pick the line that sounds like you.
- You mix up the two methods: begin with choosing substitution or elimination.
- Three unknowns feel like a maze: start with the three-unknown lesson.
- Squared terms confuse you: start with the linear-nonlinear lesson.
- Word problem answers look odd: finish with rejecting invalid solutions.
When you have read the lessons, test the whole chapter with the systems of equations practice set. If you want a teacher to watch your algebra on mixed questions, see online one-to-one Additional Mathematics tuition.