Question

lexi and daniela play a game in which they earn the same number of points for each goal and los the same number of points for each penalty. lexi makes 6 goals and 3 penalties ending the game with 6 points. daniela earns 8 goals and 9 penalties and ends the game with -22 points. I need to know the system of equations, graph it, determine number of solutions, and what the solution means

Answer 1

The system of equations is:

6x + 3y = 6

8x + 9y = -22

The graph is attached down

The number of the solutions is 1

The solution of the system is (4 , -6)

The solution means they earn 4 points for each goal and lose 6 points for each penalty

Step-by-step explanation:

Lexi and Daniela 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

• Lexi makes 6 goals and 3 penalties ending the game with 6 points
• Daniela earns 8 goals and 9 penalties and ends the game with -22 points

We need to write an system of equations represent this situation, solve it, graph it and then explain the meaning of solution

Assume that they earn x points of each goal and lose y points for each penalty

∵ x represents the score of each goal

∵ y represents the score of each penalty

∵ Lexi makes 6 goals and 3 penalties ending with 6 points

- Multiply x by 6 and y by 3, then add the products and

   equate the sum by 6

∴ 6x + 3y = 6 ⇒ (1)

∵ Daniela earns 8 goals and 9 penalties and ends the game

   with -22 points

- Multiply x by 8 and y by 9, then add the products and equate

  the sum by -22

∴ 8x + 9y = -22 ⇒ (2)

The system of equations is:

6x + 3y = 6

8x + 9y = -22

The graph is attached down

Now let us solve it

Multiply equation (1) by -3 to eliminate y

∵ -18x - 9y = -18 ⇒ (3)

- Add equations (2) and (3)

∴ (8x - 18x) + (9y - 9y) = (-22 + -18)

∴ -10x = -40

- Divide both sides by -10

∴ x = 4

- Substitute the value of x in equation (1) to find y

∵ 6(4) + 3y = 6

∴ 24 + 3y = 6

- Subtract 24 from both sides

∴ 3y = -18

- Divide both sides by 3

∴ y = -6

The number of the solutions is 1

The solution of the system is (4 , -6)

∵ x represents the score of each goal

∵ y represents the score of each penalty

∴ The score of each goal is 4 points

∴ The score of each penalty is -6

The solution means they earn 4 points for each goal and lose 6 points for each penalty

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

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