Digits, Grade 8, Volume 1, Homework Helper

#### Part 1

Example Solving Systems of Simultaneous Linear Equations

A piece of glass with an initial temperature of 99°C is cooled at a rate of 3.5°C per minute. At the same time, a piece of copper with an initial temperature of 0°C is heated at a rate of 2.5°C per minute. Let t = the temperature in degrees Celsius and m = the time in minutes.

• a. Which method would be the most efficient to use to solve the system of simultaneous linear equations?

t = 99 − 3.5m

t = 0 + 2.5m

• b. When will both objects reach the same temperature? What is the temperature?

Solution

• Step 1 Analyze the system and decide on a method.

t = 99 − 3.5m

t = 0 + 2.5m

Since both equations are in “t = ” form, use the Substitution Method.

• Step 2 Apply your method.

table with 4 rows and 3 columns , row1 column 1 , cap write , , the , , first , . equehtion . . , column 2 t , column 3 equals 99 minus 3.5 m , row2 column 1 , cap substitute . 2 . . 5 , bold italic m . , for , . bold italic t . , column 2 2.5 m , column 3 equals 99 minus 3.5 m , row3 column 1 , dd 3 . . 5 , bold italic m . to , eehch , , side . . , column 2 6 m , column 3 equals 99 , row4 column 1 , cap divide , , eehch , , side , by 6 . . , column 2 m , column 3 equals , 16.5 , end table

Substitute 16.5 for m in either equation and solve for t.

table with 3 rows and 3 columns , row1 column 1 , cap write , , either , . equehtion . . , column 2 t , column 3 equals 0 plus 2.5 m , row2 column 1 , cap substitute . 1 6 . . 5 , for , . bold italic m . , column 2 t , column 3 equals 2.5 open , 16.5 , close , row3 column 1 , cap simplify , . , column 2 t , column 3 equals , 41.25 , end table

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