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# Substitution

### Solving system of linear equations by substitution

Solve by substitution. x+y=3 x=2y | (2y)+y=3 3y=3 y=1 x=2(1) x=2 (2,1) |

Solve by substitution. x+y=6 y=-3x | x+(-3x)=6 x-3x=6 -2x=6 x=-3 y=-3(-3) y=9 (-3,9) |

Solve by substitution. y=2x+9 y=7x+10 | 7x+10=2x+9 5x=-1 x=-1/5 y=2(-1/5)+9 y=-2/5+9 y=-2/5+45/5 y=43/5 (-1/5,43/5) |

Solve by substitution. x+2y=6 2x+3y=8 | x+2y=6 x=6-2y 2(6-2y)+3y=8 12-4y+3y=8 12-y=8 -y=-4 y=4 x+2(4)=6 x+8=6 x=-2 (-2,4) |

Solve by substitution. x+2y+5=-4+5y-x 2x+x=y+4 | Simplify each equation. solve one equation for one of the variables. Substitute the expression for variable in the other equation. Simplify and solve for variable. Insert found variable into equation to find the other variable. (3,5) x=3 y=5 |

How do you check your solutions? | Insert the solutions for the variables in the original equation. |

Solve by substitution. 3x+6y=9 4x+8y=16 | 3x+6y=9 3x=9-6y x=3-2y 4(3-2y)+8y=16 12-8y+8y=16 12=16 No solution; { } |

Solve by substitution. 1/3x-y=2 x-3y=6 | When rearranged the equations are the same, meaning there are an infinite number of solutions. |

What does the false statement 3=0 imply? | The system has no solution and the lines are parallel. |

Solve by substitution. 3x-y=1 2x-3y=10 | 3x-y=1 -y=1-3x y=-1+3x 2x-3(-1+3x)=10 2x+3-9x=10 -7x+3=10 -7x=7 x=-1 2(-1)-3y=10 -2-3y=10 -3y=12 y=-4 (-1,-4) |