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# Module 5

### Solving systems of linear equations by graphing and substitution

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

Determine which ordered pair is a solution x+y=8 3x+2y=21 a- (2,4) b- (5,3) | b (5,3) |

Determine which ordered pair is a solution 3x-y=5 x+2y=11 a- (3, 4) b- (0, -5) | a (3, 4) |

Determine which ordered pair is a solution 2x+y=5 x+3y=5 a- (5, 0) b- (2, 1) | b (2, 1) |

Determine the number of solutions of a system 4x+y=24 x+2y=2 | The system has one solution it is intersecting lines. |

Determine the number of solutions of a system 2x+y=0 2y=x-4x | The system has no solution and is parallel lines. |

Use the substitution method to solve the system x+y=3 x=2y 2y+y=3 combine like terms 3y=3 divide both sides by 3 y=1 use y=1 in x=2y equation x=2(1) x=2 | (2, 1) |

Use the substitution method to solve the system x+y=6 y=-3x x+(-3x)=6 combine like terms -2x=6 divide both sides by -2 x=-3 substitute x=-3 into y=-3x equation y=-3(-3) y=9 | (-3, 9) |

Solve the system by graphing x+y=4 x-y=2 | x+y=4 substitute 0 for x 0+y=4 (0, 4) substitute 0 for y x+0=4 (4,0) x-y=2 substitute 0 for x 0-y=2 (0,-2) substitute 0 for y x-0=2 (2,0) The graph would intersect at (3,1) (I am unable to put a graph in the flash cards sorry) |

Solve the system by graphing x+y=6 -x+y=-6 | x+y=6 substitute 0 for x 0=y=6 (0,6) substitute 0 for y x+0=6 (6,0) -x+y=-6 substitute 0 for x -0+y=-6 (0,-6) substitute 0 for y -x+0=-6 (6,0) The graph would intersect at (6,0) ( I am unable to put a graph into the flash cards sorry) |

Solve by substitution y=3x+1 4y-8x=12 | 4y-8x=12 put y=3x+1 into the first equation 4(3x+1)-8x=12 distribute 12x+4-8x=12 combine like terms 4x+4=12 subtract 4 from both sides 4x=8 divide both sides by 4 x=2 put x=2 into y=3x+1 y=3(2)+1 distribute y=6+1 y=7 (2,7) |

Created by:
michellewright85