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

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jtellezd jtellezd · Answer 1 · 2020-03-05T02:32:51+01:00

Answer:

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