Question

Brayden, Howard, and Vincent are on the football team. During a game, Brayden gains 1 less than 5 times the average number of yards gained per play during the game. Howard runs for 1 more than 5 times the average number of yards gained per play during the game. Vincent runs for 5 more than 4 times the average number of yards gained per play during the game. In this activity, you will write equations to describe this situation and determine whether the equations have one solution, no solution, or infinitely many solutions.
Question 1
Part A : Write an expression for each player’s yards gained in terms of y, the average number of yards gained per play during the game.

Answer 1

Answer:  If two pair is parallel then it has no solution.

Step-by-step explanation:

Since we have given that

Let the number of gained yards by each player be y

For the case of Brayden:

Equation will be

$y=5x-1\\\\y-5x=-1$

For the case of Howard :

Equation will be

$y=5x+1\\\\y-5x=1$

For the case of Vincent :

$y=4x+5\\\\y-4x=5$

Since First two equations are parallel so it has no solution.

Reason:

$y-5x=1\\\\y-5x=-1\\\\\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\\\\\frac{1}{1}=\frac{5}{5}\neq \frac{1}{-1}$

Hence, if two pair is parallel then it has no solution.

Answer 2

Brayden: 5y - 1

Howard: 5y + 1

Vincent: 4y + 5

Explanation: I used the other answer and got it wrong. The site that I was on told me what the answer is and this was it.