okay so i really need help please help i dont understand how to do this ive asked my teacher and i still dont understand is there an easier way to do this to where i could understand? 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.
B = 5 a - 1
H = 5 a + 1
V = 4 a + 5
there is not enough information to determine (a) , so there are an infinite number of solutions
Write an equation to find the average number of yards gained per play if Brayden and Howard gained the same number of yards.
this is a good answer thank you so much Michael and scott
To solve this problem, you need to write equations that describe the situation for each player. Let's break it down step by step:
Step 1: Define variables
Let's define some variables to represent the average number of yards gained per play during the game. We can call this variable "x".
Step 2: Define equations for each player
According to the problem, Brayden gains 1 less than 5 times the average yards gained per play. So, the equation for Brayden would be:
Brayden's yards = 5x - 1
Similarly, Howard runs for 1 more than 5 times the average yards gained per play. So, the equation for Howard would be:
Howard's yards = 5x + 1
Finally, Vincent runs for 5 more than 4 times the average yards gained per play. So, the equation for Vincent would be:
Vincent's yards = 4x + 5
Step 3: Analyze the equations
Now, you need to determine whether the equations have one solution, no solution, or infinitely many solutions. One way to do this is to graph the equations on a coordinate plane. If the lines intersect at a single point, there is one solution. If the lines are parallel and do not intersect, there is no solution. If the lines are coincident and overlap, there are infinitely many solutions.
Alternatively, you can solve the system of equations algebraically by setting up a system of linear equations and using methods like substitution or elimination to find the solution (or lack thereof).
By analyzing the equations and their coefficients, it appears that the equations do not have a unique solution, and there are infinitely many possible solutions based on the variables used.
I hope this breakdown helps you understand the problem better, and please let me know if you have any further questions!