Katelyn is training for a marathon. This week she ran 6 miles less than 2 times the number of miles she ran the previous week. She ran a total of 42 miles in the two weeks.

Which system of equations can be used to find the number of miles she ran this week, r, and the number of miles she ran the previous week,

p?

The system of Equations =

r = 2p - 6 Equation 1

r + p = 42 Equation 2

Hence:

the number of miles she ran this week = r = 26 miles

the number of miles she ran the previous week = p = 16 miles

Step-by-step explanation:

Let the number of miles:

the number of miles she ran this week = r

the number of miles she ran the previous week = p

Katelyn is training for a marathon. This week she ran 6 miles less than 2 times the number of miles she ran the previous week.

r = 2 × p - 6 miles

r = 2p - 6 Equation 1

She ran a total of 42 miles in the two weeks.

r + p = 42 miles

r + p = 42 Equation 2

Which system of equations can be used to find the number of miles she ran this week, r, and the number of miles she ran the previous week,p?

The system of Equations =

r = 2p - 6 Equation 1

r + p = 42 Equation 2

We substitute 2p - 6 for r in Equation 2

2p - 6 + p = 42

3p = 42 + 6

3p = 48

p = 48/3

p = 16 miles

Solving for r

r = 2p - 6 Equation 1

r = 2(16) - 6

r = 32 - 6

r = 26 miles

Hence:

the number of miles she ran this week = r = 26 miles

the number of miles she ran the previous week = p = 16 miles

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.