Clare and Hoah 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 describe Clare and Hoahs outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty

The system

6*x  - 3*y  =  6

8*x  -  9*y  =  - 22

Solution:

x = 4

y = 6

Step-by-step explanation:

We have:

"x" number of points for a goal

"y" number of points for a penalty

Then according to problem statement, we get the two equation system

Clare       6*x  - 3*y  = 6       And

Hoah      8*x  -  9*y  =  - 22

If we are going to solve it, we can:

6*x  - 3*y  =  6      ⇒    2*x  - y  = 2

                              8*x  -  9*y  =  - 22

y = 2*x - 2

8*x  - 9 *( 2*x -2)  =  - 22    ⇒    8*x - 18*x + 18  =  - 22

-10*x = - 40       x = 4

And then  y =  2*x - 2      ⇒   y  =  8 - 2    ⇒  y  = 6