lesson
Scale an equation before eliminating
1 · Learn
When coefficients do not initially match, multiply an entire equation by a non-zero number to create a pair that can eliminate one unknown. Every term, including the constant, must be multiplied.
Substitute the resulting pair into both originals. A sign or scaling error may still produce neat numbers, so neatness is not a check.
2 · Worked example
2x + y = 11 and x - y = 1 add directly to 3x = 12. Hence x = 4 and y = 3.
3 · Your turn
Solve 2x + y = 13 and x - y = 2.
Check your answer
x = 5, y = 3.
4 · Apply your learning
Explain each equivalent transformation and verify both original equations numerically.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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