The given system is

3x + 5y | = | 8 | ... (1) |

5x + 3y | = | 0 | ... (2) |

To eliminate y, we need to make the coefficients of y the same numerical value, but with opposite sign. We can do this as follows.

3x + 5y | = | 8 | -3 |

5x + 3y | = | 0 | 5 |

-9x - 15y | = | -24 |

25x + 15y | = | 0 |

Adding these equations then eliminates y.

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