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# Module 5-

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

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

What is the solution to the following system of linear equations: * Line 1: y=3x – 1 * Line 2: y= x – 5 | Set the Two Equations Equal to each other then solve for x 1) Substitute the x value, -2, into either equation to determine y coordinate of solution 2) y=(-2) - 5 or -7 3) The solution is the point (-2, -7) |

Set the two equations equal to calculate the solution to the system below: * Line 1: y= x + 1 * Line 2: y= 2x | y= x + 1 and y= 2x x+1 = 2x -x -x 1=x y=2(1) y=2 solution= (1,2) The solution of this system is the point of intersection : (1,2) |

Solve the following system of linear equations by graphing. * 2y = 4x + 2 * and 2y = -x + 7 | * 2y = 4x + 2 o ½(2y) = ½(4x + 2) o y = 2x +1 * 2y = 8x - 2 o ½(2y) = ½(8x - 2) o y = 4x – 1 the solution of the point is (1,3) |

Solve the following system by substitution. y = 36 – 9x 3x + y/3 = 12 | 3x + (36 – 9x)/3 = 12 3x + 12 – 3x = 12 12 = 12 solution: y = 36 – 9x |

solve for one variable. 6x + 2y = 9 and 4x + y - 5 = 10. | 6x + 2y = 9 ,4x + y - 5 = 10 [ - 4x] 4x + y - 5 = 10 [ - 4x] y - 5 [ + 5] = 10 - 4x + 5 y = 10 - 4x + 5 6x + 2y = 9 6x +2(10 - 4x + 5) = 9 6x + 20 - 8x +10 = 9 [ - 30] -2x + 30 = 9 [ - 30] - 2x = - 21 x = 10.5 y = - 27 |

solve this system of equations and check. y - 2x = 11 y + 2x = 9 | 3y - 2x = 11 y = 9 - 2x 3(9 - 2x) - 2x = 11 (27 - 6x) - 2x = 11 27 - 6x - 2x = 11 27 - 8x = 11 -8x = -16 x =2 |

Solve the following system: x + y = 11 3x - y = 5 | Now, substitute 11 - x for y in the second equation 3x - (11 - x) = 5 3x - 11 + x = 5 4x = 16 x = 4 Now, substitute 4 for x 4 + y = 11 y = 7 (4, 7) |

Example: Which of the ordered pairs in the set {(5, 4),(3, 8),(6, 4),(4, 6),(7, 2)} is a solution of the following system of equations: y + 2x = 14 xy = 24 | (5, 4) is a solution of the first equation. (3, 8) is a solution of both equations. (6, 4) is a solution of the second equation. (4, 6) is a solution of both equations. (7, 2) is not a solution. The solution set of the system is {(3, 8),(4, |

Created by:
cmurrx