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# Module 5

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

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

Solve this by graphing. X=-1 Y=3 | We have X=-1 which is (-1,0) and Y=3 which is (0,3). By graphing these lines, you will see they intersect. The point they intersect is the answer. (-1,3) |

Solve by graphing. 3X+Y=6, 9X=-3Y+9 | Make a table with X and Y and use random numbers to solve for Y. Use up to 3 numbers. Do this for both equations then graph your points. In this problem, the lines are parallel and therefore they don't intersect so there is no solution. |

Without graphing, decide if these equations intersect, are parallel, or are identical on a graph and how many solutions are there. 4X+Y=24, X+5Y=5 | First step is to put these into y-intercept form. After doing so, we now compare the slopes of both equations. The slopes are different for both so it means they will intersect at one point which means there is one solution. |

Without graphing, decide if these equations intersect, are parallel, or are identical on a graph and how many solutions are there. 6X-Y=3, 1/3Y=-1+2x | Put both of these into y-intercept form. Comparing the slopes, there are both the same. Compare the y-intercepts and notice that they are also the same. Therefore the lines are identical and have infinite solutions. |

Solve by graphing. Y=-X-5, Y=2X+1 | Create two tables, one for each equation with X and Y columns. Use random numbers for X to solve for Y. Graph two points for each equation and find the intersecting point. The intersecting point is (-2,3) which is the correct answer. |

Solve by graphing. Y-5x=-5, -10x+2Y=-10 | Create the two tables with X and Y columns and solve for Y by using random numbers for X. Graph at least two points for each equation. Notice the lines are identical to each other which means the equations have infinite solutions. |

Solve by substitution. X+Y=12, X=3Y | Since we have X=3Y, we can substitute this in place of X in the first equation. Now you can solve for Y and after doing so you can solve for X. The answer is (9,3). |

Solve by substitution. 3X+15Y=18, 4X+20Y=36 | Make the first equation X= by subtracting 15Y and dividing by 3. Then substitute this in place of X in the second equation. Solve for Y. You'll notice that Y gets canceled out and your left with 24=36. This means there is no solution. |

Solve by substitution. 1/7X-Y=5, X-7Y=35 | First using the second equation, add 7Y to both sides letting X=35+7Y. Substitute this for X in the first equation and solve for Y. Notice Y gets canceled out and your left with 5=5. This means there are infinite solutions. |

Determine if the ordered pairs are solutions. A.(3,1) B.(1,3) X+Y=4, 3X+2Y=9 | Substitue the ordered pairs for X and Y appropriately. If the left side of the equations equals the right side then the pair is a solution. A.No B.Yes |

Created by:
Sabrina Hana