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# Module 5

### Solving systems of Linear Equations by Graphing and Substitution

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

Solve the equation by graphing. 2x+y=0 3x+y=1 | 2x+y=0 3x+y=1 X y 0 0 1 -2 -1 4 |

Solve the linear eguation by graphing. X+y=5 x+y=6 | x+y=5 x+y=6 x y 0 5 2 3 1 4 |

Solve by substitution method this equation. 2x-3y=6 x=2y | 2x-3y=6 x=2y substitute 2y in front of 2 therefor the eqution is as follow 2(2y)-3y=6 Foil2 times 2y 4y-3y=6 subtract 4y-3y then y=6 Now substitute in the second equation, x=2(6) Then x equals 12 The order pair is (12,6) |

Solve X+y=8 Y=5x | x+y=8 y=-5x x+(-5x)=8 x-5x=8 -4x=8 x=-2 |

Solve by Substitution 3x-y=1 2x-3y=10 | 3x-y=1 2x-3y=10 -1(-y=-3x-1)-1 y=3x-1 2x-3(3x-1)=10 2x -9x+3=10 -7x+3=10 -7x=7 x=-1 3(-1)-y=1 -3-y=1+3 +3 -1(-y=4)-1 y=4 The order pair is (-1,4) |

Is the linear equation a solution? 3x+6y=9 4x+8y=16 | 3x+6y=9 4x+8y=16 3x/3+6y/3=9/3 x+2y=3 x=-2y+3 4(-2y+3)+8y=16 -8y+12+8y=16 12=16 No solution |

is the linear equation a solution? 1/3x-y=2 x-3y=6 | 1/3x-y=2 x-3y=6 x=3y+6 1/3x(3y+6)-y=2 y+2-y=2 2=2 True solution |

Solve the system X+2y=7 2x+2y=13 | X+2y=7 X=7-2y 2x+2y=13 2(7-2y)+2y=13 14-4y+2y=13 14-2y=13 -2y=-1 Y=1/2 To find x we let y =1/2 X=7-2y X=7-2(1/2) X=7-1 X=6 |

Solve the system 7x-3y=-14 -3x+y=6 | -3x+y=6 Y=3x+6 7x-3y=14 7x-3(3x+6)=-14 7x-9x-18=-14 -2x-18=-14 -2x=4 X=-2 Now substitute -2 for x in the equation y=3x+6 then y is 0 (-2,0) the order pair |

Solve the equation by graphing. X-y=3 -x+y=-3 | x-y=3 -y=-x+3 Divide by -1 both sides Y=x+3 The equations are identical they have infinite numbers of solutions |