Question

A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume g represents the number of goals and a represents the number of assists. G a = 24. G 2 a = 42. G a = 24. 2 g a = 42. G a = 42. G 2 a = 24. G a = 42. 2 g a = 24.

Answer 1

To determine the number of goals and assists the player has, we can set up a system of equations using the given information. By solving the system of equations, we find that the player has scored 18 goals and 6 assists.

Step-by-step explanation:

In this problem, we can set up a system of equations to determine the number of goals and assists the player has. Let g represent the number of goals and a represent the number of assists. According to the given information, the combined number of goals and assists is 24, and the total number of points is 42. Since a player gets 2 points for a goal and 1 point for an assist, we can set up the following equations:

Equation 1: g + a = 24

Equation 2: 2g + a = 42

We can solve this system of equations by either substitution or elimination. Let's use elimination:

Multiply Equation 1 by 2:

2(g + a) = 2(24)

2g + 2a = 48

Now subtract this equation from Equation 2:

(2g + a) - (2g + 2a) = 42 - 48

-a = -6

Divide both sides by -1:

a = 6

Substitute this value of a back into Equation 1 to solve for g:

g + 6 = 24

g = 18

Therefore, the player has scored 18 goals and 6 assists.