Question

Jon and Kristen are both increasing the number of minutes they jog each day, as shown in the tables.

Jon
Day Minutes
0 15
1 17
2 19
3 21
Kristen
Day Minutes
0 22
1 23
2 24
3 25

Which system of linear equations could be used to determine which day they will jog for the same number of minutes, where d represents the day and m represents the number of minutes?

Answer 1

The answer is in the picture below!

Answer 2

A system of linear equations that could be used to determine which day they will jog the same number of minutes is presented as follows;

m = 2·d + 15

m = d + 22

Explanation:

The table of values for the number of minutes Jon and Kristen jog each day is presented as follows;

Jon

`\begin{array}{ccc}Day&&Minutes\\0&&15\\1&&17\\2&&19\\3&&21\end{array}`

Kristen

`\begin{array}{ccc}Day&&Minutes\\0&&22\\1&&23\\2&&24\\3&&25\end{array}`

The slope of the data representing Jon's data, m = (21 - 15)/(3 - 0) = 2

Therefore, the equation representing Jon's data is given as follows;

m - 15 = 2·d

m = 2·d + 15

The slope of the data representing Kristen's data, m = (25 - 22)/(3 - 0) = 1

Therefore, the equation representing Kristen's data is given as follows;

m - 22 = d

∴ m = d + 22

The system of linear equations that could be used to determine which day they will jog the same number of minutes is therefore;

m = 2·d + 15

m = d + 22