A system of linear equations can be solved

algebraically using **substitution** or **elimination**.

**Substitution** is a method for solving a system of equations where a variable is replaced by the expression it is equal to.

Substitution is a good method for solving a system of linear equations when one of the equations can easily be solved for one of the variables.

First, use opposite operations to solve the first equation for

*x*.

*x* + 4*y* - 4*y* | = | 37 - 4*y* |

*x* | = | 37 - 4*y* |

Next, substitute

*x* = 37 - 4

*y* into the second equation, and solve for

*y*.

2(37 - 4*y*) - 2*y* | = | -6 |

74 - 8*y* - 2*y* | = | -6 |

74 - 10*y* | = | -6 |

74 - 10*y* - 74 | = | -6 - 74 |

-10*y* | = | -80 |

-10*y* ÷ (-10) | = | -80 ÷ (-10) |

*y* | = | 8 |

Then, substitute

*y* = 8 into the first equation, and solve for

*x*.

*x* + 4(8) | = | 37 |

*x* + 32 | = | 37 |

*x* + 32 - 32 | = | 37 - 32 |

*x* | = | 5 |

So, *x* = 5 and *y* = 8.

**Elimination** is a method for solving a system of equations where the equations, or multiples of the equations, are added or subtracted in order to eliminate one variable.

Elimination is a good method for solving a system of linear equations when one of the variables has the same coefficient in both equations.

First, subtract the second equation from the first to cancel out the

*x* terms.

Next, substitute

*y* = -2 into the second equation, and solve for

*x*.

3*x* - (-2) | = | 14 |

3*x* + 2 | = | 14 |

3*x* + 2 - 2 | = | 14 - 2 |

3*x* | = | 12 |

3*x* ÷ 3 | = | 12 ÷ 3 |

*x* | = | 4 |

So, *x* = 4 and *y* = -2.