Question

Clare and Noah 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. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points.

Write a system of equations that describes Clare and Noah's outcomes. Use x to represent the number of points for a goal and to y to represent the number of points for a penalty.

Solve the system. What does your solution mean?

Answer 1

Point per goal --- x
points per penalty --- y

Clare: 6x + 3y = 6 ---> 2x + y = 2 OR y = 2 - 2x
Noah: 8x + 9y = -22

using substituion:
8x + 9(2-2x) = -22
8x + 18 - 18x = -22
-10x = -40
x = 4
then y = 2 - 2(4) = -6

your turn to show what that means.

Answer 2

what would y equal?