Question

Ben and Alyssa play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Ben makes 7 goals and 2 penalties, ending the game with 21 points. Alyssa earns 10 goals and 8 penalties and ends the game with

Use a system of equations to solve the following:

A. penalty earns____points
B. goal earns____points

Answer 1

To find the points for a goal and a penalty in Ben and Alyssa's game, a system of equations is set up with variables x for points per goal and y for points per penalty. The equations are based on Ben's final score and assume Alyssa's final score is given. Without Alyssa's exact final score, we cannot solve for x and y.

Step-by-step explanation:

To solve for the points earned by a goal and the points lost by a penalty, we can set up a system of equations based on the information given for Ben and Alyssa's game scores.

Let x represent the number of points per goal, and y represent the number of points per penalty. We have two equations:

1. 
   
3. 
   

However, we cannot solve this system of equations without knowing Alyssa's final score. Assuming Alyssa's final score is provided as z, the system becomes:

1. 
   
3. 7x - 2y = 21
4. 
   
6. 10x - 8y = z

Let's solve the system using the first equation:

Isolate y in terms of x from the first equation:

2y = 7x - 21

y = (7x - 21)/2

Now substitute y in the second equation and solve for x once the value of z is known:

10x - 8((7x - 21)/2) = z

10x - 4(7x - 21) = z

...

Unfortunately, without Alyssa's final score or more information, we cannot determine the exact values of x and y.