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# Module 6 Study Stack

### Flash Cards for Module 6

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

Solve the system of equations using the addition method:<br> 6x+y=15<br> 4x-y=5 | y and -y cancel each other out. Add 6x+ 4x to get 10x and 15 +5 to get 20. So your equation should now look like 10x=20. Divide both sides by 10 and x=2. Plug 2 in for x in either equation. Ex: 6(2)+y=15 simplify, 12+y=15 subtract 12 from both sides, y=3. |

Solve the system of equations using the addition method:<br> x-5y=-8<br> -x+4y=6 | X and -X Cancel. Add -5y+4y and -8+6. Your new equation should look like -y=-2. Divide both sides by -1 and y=2. Plug y into either equation and solve for x. Ex. x-5(2)=-8, x-10=-8, x=2. Write as an ordered pair (2,2) |

Solve the system of equations using the addition method:<br> 3x+5y=-7<br> 4x-5y=-21 | 5y and -5y cancel out. Add 3x+4x and -7+-21 to get 7x=-28. Divide both sides by 7. x=-4. Plug -4 in for x in either equation. Ex. 3(-4)+5y=-7, -12+5y=-7, 5y=5, y=1. Write as an ordered pair (-4,1). |

Solve the system of equations using the addition method:<br> x+3y=2<br> 6x+5y=-14 | Multiply the first equation entirely by -6 so it becomes -6x-18y=-12. 6x and -6x cancel. add both sides of the equations together. 5y-18y=-12-14, -13y=-26, divide by -13, y=2. Plug y into either equation, x+3(2)=2, x+6=2, x=-4. (-4,2). |

Solve the system of equations using the addition method:<br> x-y=-10<br> x+y=-4 | -y and y cancel. Add both sides of the equations together. x+x=-10-4, 2x=-14, divide both sides by 2, x=-7. Plug -7 in for x in either equation. -7-y=-10, -y=-3, y=3. (-7,3). |

Solve the system of equations:<br> x-y+z=-8<br> 4x+2y-z=12<br> -2x+4y-z=36 | Combine equations 1 and 2. x+4x-y+2y=-8+12, 5x+y=4. This is equation 4. Multiply equation 2 by -1 and combine with equation 3 to get rid of z again. -4x-2x-2y+4y=-12+36, -6x+2y=24. This is equation 5. Multiply equation 4 by -2 to get -10x+-2y=-8... |

Cont..Solve the system of equations:<br> x-y+z=-8<br> 4x+2y-z=12<br> -2x+4y-z=36 | Cont...Combine with equation 5. -16x=16, x=-1. Plug -1 in for x into either equation 4 or 5, -6(-1)+2y=24, 6+2y=24, 2y=18, y=9. Plug x and y into euqation 2 4(-1)+2(9)-z=12, -4+18-z=12, 14-z=12, -z=-2, z=2. (-1,9,2). |

Solve the system of equations:<br> x+y=1<br> 6y=18<br> 2x+3y-2z=-3 | 6y=18, divide both sides by 6, y=3. Plug 3 into the first equation for y. x+3=1, x=-2. Plug x and y into equation 3, 2(-2)+3(3)-2z=-3, -4+9-2z=-3, 5-2z=-3, -2z=-8, z=4. (-2,3,4) |

Solve the system of equations:<br> 2x+8y+z=27<br> -x+y+3z=-4<br> x+4y+4z=3 | Multiply equation 2 by 2 to get -2x+2y+6z=-8. Combine with equation 1. 10y+7z=19 this is equation 4. Combine equation 2 and 3. 5y+7z=-1 this is equation 5. Multiply euation 5 by -2 to get -10x-14z=2 combine with equation 4 -7z=21, z=-3. Plug z into 4... |

Cont... | or 5, 10y+7(-3)=19 10y-21=19, 10y=40, y=4. Plug both y and z into equation 2. -x+4+3(-3)=-4, -x+4-9=-4, -x-5=-4, -x=1, x=-1. (-1,4,-3) |

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