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
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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