The equation is 4x+8y=20 and -4x+2y=-30 where I am told to find X and Y using elimination. Anyone have any ideas?

OwenT154
Jan 4, 2018

#1**+2 **

Let's line the equation up side by side.

\(\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\)

Take note of the bit highlighted in red. Do you notice how the coefficients are opposite of each other? This is important! If I were to add these equations together as is, then the x would cancel out.

\(\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\\ \overline{\quad\quad\quad\quad\quad\quad\quad\quad}\\ \hspace{2mm}0x+10y=-10\)

We can solve for y pretty easily by dividing by -10. Of course, 0x simplifies to 0, so the x has disappeared.

\(10y=-10\\ \hspace{5mm}y=-1\)

We can now plug in this y value into the the original equation and solve for x. I'll plug it into the first one.

\(4x+8y=20\) | We already know that y=-1, so let's substitute that in for y and solve for the remaining unknown. |

\(4x+8(-1)=20\) | 8*-1 can be simplified. |

\(4x-8=20\) | Add 8 to both sides. |

\(4x=28\) | Finally, divide by 4 to isolate x completely. |

\(x=7\) | |

TheXSquaredFactor
Jan 4, 2018

#1**+2 **

Best Answer

Let's line the equation up side by side.

\(\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\)

Take note of the bit highlighted in red. Do you notice how the coefficients are opposite of each other? This is important! If I were to add these equations together as is, then the x would cancel out.

\(\hspace{4mm}\textcolor{red}{4x}+8y=+20\\ \textcolor{red}{-4x}+2y=-30\\ \overline{\quad\quad\quad\quad\quad\quad\quad\quad}\\ \hspace{2mm}0x+10y=-10\)

We can solve for y pretty easily by dividing by -10. Of course, 0x simplifies to 0, so the x has disappeared.

\(10y=-10\\ \hspace{5mm}y=-1\)

We can now plug in this y value into the the original equation and solve for x. I'll plug it into the first one.

\(4x+8y=20\) | We already know that y=-1, so let's substitute that in for y and solve for the remaining unknown. |

\(4x+8(-1)=20\) | 8*-1 can be simplified. |

\(4x-8=20\) | Add 8 to both sides. |

\(4x=28\) | Finally, divide by 4 to isolate x completely. |

\(x=7\) | |

TheXSquaredFactor
Jan 4, 2018