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# Module 7

### Solving systems of linear equations

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

A first number is 5 more than the second number. Twice the first number is 2 less than 3 times the second number. | x=y+5 (1st #) 2x=3y-2 (2nd #) Use the substitution method Answer: (17,12) |

Admission tickets at the Livonia spree for 2 adults and 4 kids are $34, and $31 for 3 adults and 2 kids. Find the price for adults and kids. | 2x+4y=34 3x+2y=31 Use the elimination method to solve. x=7 y=5 Adult=$7 Kid=$5 |

A new cupcake shop opened up on Haggerty. The owners purchased $1,000 worth of ingredients to make delicious cupcakes. Each cupcake cost $1 to make and are sold for $2. When does the shop break even? | R(x)=2*x C(x)=1*x+1,000 2x=1x+1,000 x=1,000 1,000 cupcakes must be sold to break even. |

The measure of the largest angle of a triangle is 40 degrees more than the measure of the smallest angle and the measure of the remaining angle is 20 degrees more than the measure of the smallest angle. What is the measure of each angle? | Sum of triangle as equation 1 x+y+z=180 y=x+40 z=x+20 Use the substitution method to solve. x=40 y=80 z=60 (40,80,60) |

Two cars leave Yellowstone National park at the same time, one going east the other going west. After 4 hours the cars were 520 miles apart. If the car headed west is traveling 10 miles faster than the car headed east, at what rate are they driving? | x=west y=east (time multiplied by unknown rate) 4x+4y=480 x=y+10 Use the substitution method to solve. West bound car 70 mph East bound car 60 mph |

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szavedyuk