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# Simultaneous Eqns

### Methods and steps for solving algebraic simultaneous equations

Question | Answer |
---|---|

Simultaneous Equations Addition/Subtraction/Elimination Method | 1. Multiply one or both equations by some number to make the number in front of one of the variables the same in each equation |

Elimination Method Example | 3x + 3y = 24 2x + y = 13 MULTIPLY bottom equation by -3 |

Elimination Method Example(Card 2) | Equations become: 3x + 3x = 24 -6x - 3y = -39 |

Elimination Method Example (Card 3) | 2. ADD the equations to eliminate the y variable. You get: -3x = -15. SOLVE for x to get x = 5. |

Elimination Method Example (Card 4) | To solve for y, plug the value x = 5 back into either original equation. EXAMPLE: 2(5) + y = 13 10 + y = 13 y = 13 - 10, so y = 3. |

Simultaneous Equations Substitution Method | For this method, you need to isolate one of the variables on one side of the equation |

Substitution Method Example (Card 1) | Let's use the equations x + y = 3 2x + 3y = 8 |

Substitution Method (Card 2) | In the first equation, move everything but the x to the right side of the equation to get: x = 3 - y |

Substitution Method (Card 3) | Now wherever there is an x in the second equation, we can substitute 3 - y. So the equation 2x + 3y = 8 becomes 2(3 - y) + 3y = 8. |

Substitution Method (Card 4) | When we simplify this, we get 6 - 2y + 3y = 8. This becomes 6 + y = 8 or y = 8 - 6 = 2 |

Substitution Method (Card 5) | Now, to solve for x, simply plug the value for y, which is 2, back into the first equation: x + 2 = 3. So, x = 1. |

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wronawoman