SM1.3 Pair of linear equations
You can solve two linear equations in two unknowns by substitution and by elimination, tell before solving whether a pair has one solution, none or infinitely many, and turn a word problem into such a pair.
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One equation in two unknowns is a line of possibilities; a second equation picks the point where the two lines meet, if they meet. Substitution and elimination are two routes to that same point, and the coefficients alone tell you in advance whether the lines cross once, run parallel, or lie on top of each other. The word problems, about ages, fares, speeds and mixtures, are the chapter's real destination, and they return in every examination after school.
Work through these
Solve the same pair of equations by substitution and again by elimination, and confirm both give one point
Doing both methods on one pair shows they are routes, not rules. From then on you can pick whichever the numbers make easier, which is a small decision that saves time on every paper.
Using only the ratios of coefficients, sort several pairs into one solution, no solution and infinitely many
The ratio test answers the question before any solving starts, and examiners love asking it on its own. Tying each verdict to its picture, crossing lines, parallel lines, the same line, keeps the three cases from blurring together.
Turn five word problems into pairs of equations before solving any of them
Setting up is the hard half and the taught half is solving, which is the wrong way round. Writing all five setups first, then solving, separates the skill that needs practice from the one you already have.
Take one solved problem and check the answer back in the words of the question, not the equations
An answer can satisfy your equations and still be wrong because the setup was wrong. Checking against the story itself is the only check that catches that, and it costs one minute.
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