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# Module 5 - Review

### Module 5 - Solving Systems of Linear Equations by Graphing and Substitution

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

A ______ __ ______ ________ consists of two or more linear equations. | system of linear equations |

Solve by graphing -x+3y=10 x+y=2 | (-1,3) |

A system of equations that has at least one solution is a _______ ________. | Consistent System |

A system that has no solution is an _______ ________. | Inconsistent System |

How many solutions do they have: a)one point of intersection b)parallel lines c)same line | a)one solution b)no solution c) infinite number of solutions |

Solve using the substitution method: 2x+y=10 x=y+2 | 2x+y=10 (first equation) 2(y+2)+y=10 (substitute y+2 for x since x=y=2) 2y+4+y=10( use distributive property) 3y+4y=10 (combine like terms) 3y=6 (subtract 4 from both sides) y=2 (divide both sides by 3) x=y+2 (second equation) x=2+2( let y=2) x |

__________ method is a method of solving a system of equations wherein one of the equations is solved for one variable in terms of the other variables. | Substitution |

Solve using the substitution method: 5x-y =-2 y =3x | 5x-y =-2 (first equation) 5x-(3x)=-2(substitute 3x for y) 2x=-2(combine like terms) x=-1(Divide both sides by 2) y=3x(second equation ) y=3(-1)(let x be -1) y=-3 Solution:(-1,-3) |

Solve using the substitution method: 6x+12y=5 -4x-8y=0 | -4x-8y=0 -8y=4x -8y/8=4x/-8 y=1/2x 6x+12y=5 6x+12(-1/2x)=5 6x+(-6x)=5 0=5 no soution |

Solve using the substitution method: 3y - 2x = 11 y + 2x = 9 | 3y - 2x = 11 3(9 - 2x) - 2x = 11 27 - 6x) - 2x = 11 27 - 6x - 2x = 11 27 - 8x = 11 -8x = -16 x = 2 y = 9 - 2x y = 9 - 2(2) y = 9 - 4 y = 5 (2,5) |

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