lesson
One pair must satisfy both rules
1 · Learn
Two simultaneous linear equations impose two conditions on the same unknowns. Elimination adds or subtracts equivalent equations to remove one unknown; substitution then finds the other.
A pair that satisfies only one equation is not a solution of the system. On a graph, a unique solution is the intersection of the two lines.
2 · Worked example
x + y = 11 and x - y = 3 add to 2x = 14. Thus x = 7 and y = 4.
3 · Your turn
Solve x + y = 9 and x - y = 1.
Check your answer
x = 5 and y = 4.
4 · Apply your learning
Plot both original lines and compare their intersection with the algebraic result.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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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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