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# Module 5

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

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

X+Y=7 2x+3y=17 A. Is (4,3) a solution? B. Is (1,6) a solution? | Substitue X and Y with the appropriate numbers. If the left side of the equation equals the right side, the answer is yes. Both answers are yes. |

Solve by graphing. X+Y=5 -X+Y=-5. | Create a table with a column for X and column for Y and use the value of X (ex: 0,1,2) to solve for Y. Each equation has its own table. Graph two points and notice where the two lines intersect. Answer is (5,0). |

Solve by substitution. X+Y=8, X=3Y | Since X=3Y, Substitute X in X+Y=8 with 3Y and solve for Y. Next plug in Y into one of the equations and get the answer for X. Solution is (6,2). |

Solve by substitution. 21X+7Y=22, -3x=Y+6 | Add -6 to both sides to the second equation so Y=-3x-6. Substitute Y in the first equation for Y=-3x-6. Solve for X and Y. You'll notice there is no solution for this equation since the X values cancel out and you're left with two integers. |

X+Y=9, 2X+3Y=21 A. Is (5,4) a solution? B. Is (6,3) a solution? | Basically substitute the solutions accordingly to their correct positions and determine if they are solutions. A. No B. Yes |

Solve by graphing. X+Y=3, X+Y=1 | Make tables for each equation using X and Y columns and substitute numbers for X (0,1,2) and solve for Y. Graph two points and notice the lines are parallel to each other and don't intersect. There is no solution. |

Solve by graphing. Y-2X=-4, -6X+3Y=-12 | Make tables for each and solve for X and Y. Graph two points for each table. Notice the two lines and the same and there are infinite solutions. |

Solve by substitution. X+10Y=36, 3X+4Y=4 | Get X to equal X=-10Y+36. Substitute X in the second equation with X=-10Y+36 and solve for Y. Plug in the answer for Y in the first equation and solve for X. Answer is (-4,4). |

Solve without graphing. X=-7, Y=9 A. Do these lines intersect? B.How many solutions does this have? | Since X=-7, this line will be horizontal. Y=9 means the line will be vertical. They will intersect at one point. A.Yes B.Yes |

Solve without graphing. 9X-Y=12, 1/3Y=-4+3X. A. Do these lines intersect? B. How many solutions does this have? | First, we want to put these equations in slope intercept form. Once that is done, we now look at the y-intercept and slope of both equations. Notice they are both the same meaning they are identical lines with infinite solutions. A.No, parallel B.Infinite |

Created by:
Ali Alaouie