How do you solve simultaneous equations by elimination?
Kurze Antwort
Make the coefficient of one letter the same in both equations, then add or subtract the equations to remove that letter. Solve for the letter that is left, then substitute it back into either original equation to find the other one.
Schritt für Schritt
- Line the equations up so x, y and the numbers are in the same columns.
- Multiply one or both equations so that x (or y) has the same coefficient in both.
- If the signs are the same, subtract the equations. If they are different, add them.
- Solve the single equation that is left.
- Substitute that value into one of the original equations to find the other unknown, then check both equations.
Beispiel
Solve 3x + 2y = 16 and x − 2y = 0
- The y terms are +2y and −2y, so add the equations
- 4x = 16, so x = 4
- Substitute into x − 2y = 0: 4 − 2y = 0, so y = 2
- Check: 3(4) + 2(2) = 16
Typische Fehler
- Multiplying only one side of an equation, or only some of its terms.
- Subtracting when the signs are different. Remember: same signs subtract, different signs add.
- Stopping after finding one unknown.
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