Solving a system of three equations
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Flip to reveal answersHow do you solve three linear equations in three unknowns by hand?
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All 8 Flashcards — Solving a system of three equations
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Question
How do you solve three linear equations in three unknowns by hand?
Answer
Eliminate one variable to get two equations in two unknowns, solve those, then back-substitute for the third.
Question
How do you eliminate a variable?
Answer
Add or subtract two equations (scaling one first if needed) so that variable cancels.
Question
How do you find the third unknown after the first two?
Answer
Back-substitute the known values into one of the original equations.
Question
How do you solve a 3×3 system on the GDC (Paper 2)?
Answer
Use the simultaneous-equation solver (PlySmlt2) or enter the coefficient matrix and use rref.
Question
What if the coefficients don't match to cancel?
Answer
Multiply an equation by a constant first so a variable's coefficients are equal (or opposite).
Question
How do you check a solution (x, y, z)?
Answer
Substitute it into the equation you didn't use last; all three should hold.
Question
Solve x + y + z = 6, x − y + z = 2, 2x + y − z = 1.
Answer
x = 1, y = 2, z = 3.
Question
Why eliminate the SAME variable from two pairs?
Answer
It leaves two equations in the same two unknowns, which you can then solve as a 2×2 system.
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Full study notes for Solving a system of three equations
Topic 1.16 hub
Systems of equations (HL only)
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